Algebra and Functions: Master the Fundamentals of Math

Question 1

Which graph represents the equation y = -2x + 1?

Accepted Answer

A line with a slope of -2 and a y-intercept of 1

Answer

A line with a slope of 2 and a y-intercept of 1

Answer

A parabola with a vertex at (1, -2)

Answer

A circle with a radius of 1 and a center at (0, 0)

Question 2

In the equation y = mx + b, 'm' represents the slope of the line. What is the slope of the line represented by the equation y = 2x + 3?

Accepted Answer

2

Answer

1

Answer

3

Answer

0

Question 3

Find the equation of a linear function with a slope of -2 and a y-intercept of 3.

Accepted Answer

y = -2x + 3

Answer

y = 2x + 3

Answer

y = 3x - 2

Answer

y = -3x + 2

Question 4

Which of the following equations represents a line with a slope of 3 and a y-intercept of 5?

Accepted Answer

y = 3x + 5

Answer

y = 5x + 3

Answer

y = 3x - 5

Answer

y = 5/3x + 5

Question 5

Identify the correct classification of the function f(x) = 3x^2 - 2x + 1.

Accepted Answer

Quadratic

Answer

Linear

Answer

Exponential

Answer

Rational

Question 6

Which graph represents the linear equation y = 2x + 1?

Accepted Answer

A line with a slope of 2 and a y-intercept of 1

Answer

A line with a slope of 1 and a y-intercept of 2

Answer

A parabola

Answer

A circle

Question 7

Given the equation y = -2x + 3, what is its graphical representation?

Accepted Answer

A line with a slope of -2 and a y-intercept of 3.

Answer

A line with a slope of 2 and a y-intercept of -3.

Answer

A line with a slope of 3 and a y-intercept of -2.

Answer

A line with a slope of -3 and a y-intercept of 2.

Question 8

Which of the following is the graph of the quadratic function f(x) = x^2 - 4x + 3?

Accepted Answer

A parabola that opens up with a vertex at (2, -1)

Answer

A parabola that opens down with a vertex at (-2, 1)

Answer

A line with a slope of -4 and a y-intercept of 3

Answer

A circle with a radius of 3 and a center at (0, 0)

Question 9

What is a defining characteristic of a linear function?

Accepted Answer

Constant rate of change

Answer

x-intercept

Answer

Nonlinear graph

Answer

Positive y-intercept

Question 10

Find the slope and y-intercept of the equation y = 2x - 5:

Accepted Answer

Slope: 2, y-intercept: -5

Answer

Slope: -5, y-intercept: 2

Answer

Slope: 2/5, y-intercept: 0

Answer

Slope: 1, y-intercept: 5

Question 11

Factor the quadratic expression: x^2 - 6x + 8

Accepted Answer

(x - 2)(x + 4)

Answer

(x - 4)(x - 2)

Answer

(x + 4)(x + 2)

Answer

(x - 8)(x - 1)

Question 12

What is the equation of the line with a slope of 2 and a y-intercept of -3?

Accepted Answer

y = 2x - 3

Answer

y = 3x - 2

Answer

y = -2x + 3

Answer

y = -3x + 2

Question 13

Find the slope of the line that passes through the points (2, 3) and (5, 7).

Accepted Answer

4/3

Answer

1

Answer

2

Answer

3/4

Question 14

Which of these linear functions has a graph with a slope of -2 and a y-intercept of 3?

Accepted Answer

f(x) = -2x + 3

Answer

f(x) = 3x - 2

Answer

f(x) = 2x + 3

Answer

f(x) = -3x + 2

Question 15

Which equation represents a linear function?

Accepted Answer

y = 3x - 5

Answer

y = x^2 + 2x + 1

Answer

y = √x + 1

Answer

y = 1/x

Question 16

Find the equation of the linear function with a slope of 2 and a y-intercept of -3.

Accepted Answer

y = 2x - 3

Answer

y = -2x + 3

Answer

x = 2y - 3

Answer

x = -2y + 3

Question 17

Find the equation of the line that passes through the points (2, 5) and (-1, -3).

Accepted Answer

y = -2x + 9

Answer

y = 2x + 1

Answer

y = x + 3

Answer

y = -x + 1

Question 18

Which graph represents the equation y = -2x + 5?

Accepted Answer

A line with a slope of -2 and a y-intercept of 5

Answer

A line with a slope of 2 and a y-intercept of 5

Answer

A parabola with a vertex at (5, 0)

Answer

A circle with a radius of 5

Question 19

Find the equation of the line passing through points (2, 3) and (5, 7).

Accepted Answer

y = 2x + 1

Answer

y = x + 1

Answer

y = x - 1

Answer

y = -2x + 1

Question 20

Find the equation of the line that passes through the points (2, -1) and (4, 3).

Accepted Answer

y = 2x - 5

Answer

y = x + 1

Answer

y = -x + 3

Answer

y = -2x + 1

Question 21

Identify the equation that represents a line with a slope of -2 and a y-intercept of 5:

Accepted Answer

y = -2x + 5

Answer

y = 2x + 5

Answer

y = 5x - 2

Answer

y = -5x + 2

Question 22

Which of the following is a key feature of a linear function?

Accepted Answer

Constant slope

Accepted Answer

Can be expressed as y = mx + b

Answer

Passes through the origin

Answer

Parabola-shaped graph

Question 23

Determine the equation of the straight line that passes through the points (2, 5) and (-4, 1).

Accepted Answer

y = -2/3x + 11/3

Answer

y = 3x + 1

Answer

y = -3x + 1

Answer

y = 2x + 5

Question 24

Which graph accurately represents the function f(x) = x^2 - 4x + 3?

Accepted Answer

Upward parabola with vertex at (2, -1)

Answer

Downward parabola with vertex at (-2, 1)

Answer

Line with slope 2 and y-intercept 3

Answer

Circle with center at (0,0) and radius 3

Question 25

Which graph represents the linear function f(x) = 2x - 1? Identify the graph that matches the function's equation and has the correct slope and y-intercept.

Accepted Answer

A line sloping upward from left to right, passing through (0, -1) with a steeper incline than a 45-degree angle

Answer

A line sloping downward from left to right, passing through (-1, 0) with a shallower incline than a 45-degree angle

Answer

A parabola opening upward with its vertex at (0, -1)

Answer

A circle centered at the origin with a radius of 1

Question 26

Which logarithmic property allows us to rewrite (log base b of a to the power of c) as (c times log base b of a)?

Accepted Answer

Power rule

Answer

Sum rule

Answer

Difference rule

Answer

Quotient rule

Question 27

Determine the equation of the line that passes through the points (2, 5) and (4, 9).

Accepted Answer

y = 2x + 1

Answer

y = x - 1

Answer

y = 3x - 1

Question 28

Consider the quadratic function f(x) = x^2 - 4x + 3. Which of the following describes its graph?

Accepted Answer

A parabola opening upward with vertex at (2, -1).

Answer

A parabola opening downward with vertex at (-2, -1).

Answer

A parabola opening upward with vertex at (2, 1).

Answer

A parabola opening downward with vertex at (-2, 1).

Question 29

Identify the linear equation from the given options:

Accepted Answer

y = 2x + 5

Answer

y = x^2 - 3

Answer

y = √x + 1

Answer

y = 1/(x-2)

Question 30

In the equation y = -2x + 5, what is the value of y when x is 0?

Accepted Answer

5

Answer

2

Answer

-2

Answer

0

Question 31

In the linear function f(x) = 2x - 5, what is the value of the y-intercept?

Accepted Answer

-5

Answer

2

Answer

5

Answer

0

Question 32

Solve the system of equations:
x + y = 5
y - x = 1

Accepted Answer

x = 2, y = 3

Answer

x = -2, y = 5

Answer

x = 3, y = 2

Answer

The system has no solution

Question 33

Simplify the rational expression: $$rac{x^2 - 2x}{x^2 - 4}$$

Accepted Answer

$x - 2$

Answer

$x$

Answer

$x + 2$

Question 34

Solve the quadratic equation: **2x² - 8 = 0**

Accepted Answer

x = 2, -2

Answer

x = 2

Answer

x = 4

Answer

x = 0

Question 35

Factor the quadratic expression: x^2 - 9

Accepted Answer

(x + 3)(x - 3)

Answer

(x - 3)(x + 3)

Answer

(x + 9)(x - 9)

Answer

(x - 9)(x + 9)

Question 36

Evaluate the quadratic function f(x) = 2x^2 - 3x + 1 at x = 2

Accepted Answer

f(2) = 5

Answer

f(2) = 1

Answer

f(2) = 3

Answer

f(2) = 7

Question 37

Identify the domain of the square root function g(x) = sqrt(x - 2)

Accepted Answer

x ≥ 2

Answer

x ≤ 2

Answer

x ≠ 2

Answer

x = 2

Question 38

Solve the linear inequality: x - 4 > 6

Accepted Answer

x > 2

Answer

x < 2

Answer

x > 10

Answer

x < 10

Question 39

Identify the graph that accurately represents the inequality x - 2y > 4.

Accepted Answer

A line with a positive slope and a shaded region below the line.

Answer

A line with a negative slope and a shaded region above the line.

Answer

A horizontal line with a shaded region above the line.

Question 40

Simplify the radical expression: √(16x²)

Accepted Answer

8x

Answer

4x

Answer

16x

Answer

32x

Question 41

Which of the following is considered a quadratic function?

Accepted Answer

f(x) = x² + 3x - 5

Answer

f(x) = x + 2

Answer

f(x) = 2x³ + 5x

Answer

f(x) = e^x

Question 42

Which graph corresponds to the function: f(x) = 2^x

Accepted Answer

Exponential

Answer

Linear

Answer

Quadratic

Answer

Logarithmic

Question 43

Solve the inequality: 2x - 5 ≤ 7

Accepted Answer

x ≤ 6

Answer

x ≥ 6

Answer

x > 6

Answer

x < 6

Question 44

In the quadratic function f(x) = ax² + bx + c, the axis of symmetry is a vertical line. Which equation represents this axis of symmetry?

Accepted Answer

x = -b/2a

Answer

y = -b/2a

Answer

x = a/2b

Answer

y = a/2b

Question 45

Solve the inequality: 2x + 5 < 15.

Accepted Answer

x < 5

Answer

x > 5

Answer

x = 5

Answer

x < 10

Question 46

To solve for x in the equation 2x + 5 = 13, what operation should you perform first?

Accepted Answer

Subtract 5 from both sides

Answer

Divide both sides by 2

Answer

Add 5 to both sides

Answer

Multiply both sides by 2

Question 47

What is the completely factored form of the expression x^2 - 9?

Accepted Answer

(x + 3)(x - 3)

Answer

(x - 3)(x - 3)

Answer

(x - 9)(x + 1)

Answer

The expression cannot be factored

Question 48

Simplify the algebraic expression (3x^2y)/(xy^3):

Accepted Answer

3x/y^2

Answer

3y/x^2

Answer

3x^3/y^2

Answer

3y^3/x^2

Question 49

What is the equation of the rational function that has a vertical asymptote at x = 2 and a horizontal asymptote at y = 1?

Accepted Answer

y = 1/(x-2)

Answer

y = 2/(x-1)

Answer

y = 1/(x+2)

Answer

y = 2/(x+1)

Question 50

Factor the quadratic expression: x^2 - 4

Accepted Answer

(x - 2)(x + 2)

Answer

(x + 2)^2

Answer

(x - 4)(x + 4)

Answer

The expression is prime

Question 51

Find the vertex of the parabola: y = x^2 - 6x + 8

Accepted Answer

(3, -1)

Answer

(3, 1)

Answer

(-3, -5)

Answer

(-3, 5)

Question 52

Solve the linear inequality: 3x - 5 > 10

Accepted Answer

x > 5

Answer

x < 5

Answer

x > -5

Answer

x < -5

Question 53

Solve the exponential equation: 2^x = 16

Accepted Answer

x = 4

Answer

x = 2

Answer

x = 8

Answer

x = 16

Question 54

Find the domain of the function: f(x) = sqrt(x - 2)

Accepted Answer

x ≥ 2

Answer

x ≤ 2

Answer

x > 2

Answer

x < 2

Question 55

Determine the range of the function: f(x) = |x|

Accepted Answer

y ≥ 0

Answer

y ≤ 0

Answer

y > 0

Answer

y < 0

Question 56

Find the domain of the following function: f(x) = 1 / (x - 3)

Accepted Answer

All real numbers except x = 3

Answer

x < 3

Answer

All real numbers

Answer

x > 3

Question 57

Find the inverse of the following function: f(x) = 3x - 2

Accepted Answer

f^-1(x) = (x + 2)/3

Answer

f^-1(x) = 2x + 3

Answer

f^-1(x) = x^3 - 2

Answer

f^-1(x) = -3x + 2

Question 58

Which of the following is the parent function of the logarithmic function f(x) = log(x + 2)?

Accepted Answer

f(x) = log(x)

Answer

f(x) = e^x

Answer

f(x) = x^2

Answer

f(x) = 2^x

Question 59

Find the coordinates of the vertex of the parabola: y = x^2 - 4x + 3

Accepted Answer

(2, -1)

Answer

(0, 3)

Answer

(-2, 1)

Answer

(4, -5)

Question 60

Solve the inequality: 2x + 5 > 13

Accepted Answer

x > 4

Answer

x > -4

Answer

x < -4

Answer

x < 4

Question 61

Determine the domain of the function: f(x) = 1/(x - 2)

Accepted Answer

All real numbers except 2

Answer

All real numbers

Answer

All positive real numbers

Question 62

Solve the linear equation: 3x + 5 = 14

Accepted Answer

x = 3

Answer

x = 6

Answer

x = 1

Answer

x = -3

Question 63

Which binomial is a factor of the polynomial x² - 5x + 6?

Accepted Answer

(x - 2)

Answer

(x - 6)

Answer

(x + 2)

Answer

(x + 1)

Question 64

What are the coordinates of the vertex of the parabola defined by the function f(x) = (x + 2)² - 3?

Accepted Answer

(-2, -3)

Answer

(-2, 3)

Answer

(2, 3)

Answer

(2, -3)