Master Functions in Algebra I: Online Quizzes and Practice

Question 1

Which equation represents a linear function with a slope of 2 and a y-intercept of -1?

Accepted Answer

y = 2x - 1

Answer

y = x^2 - 1

Answer

y = e^(2x)

Answer

y = |x + 1|

Question 2

Which graph accurately represents the quadratic function f(x) = -2x^2 + 4x - 1?

Accepted Answer

Parabola opening downwards

Answer

Parabola opening upwards

Answer

Straight line with a slope of -2

Answer

Circle

Question 3

Which graph represents the linear function f(x) = 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 with a vertex at (0, 1)

Answer

A circle with a radius of 1

Question 4

Analyze the graph of the linear function f(x) = 2x + 1. Which equation accurately represents the line shown in the graph?

Accepted Answer

y = 2x + 1

Answer

y = x - 1

Answer

y = x^2 + 1

Answer

y = 2/x + 1

Question 5

In the notation f(x) = 2x + 1, what does f(x) represent?

Accepted Answer

The output of the function for any input value of x

Answer

The input of the function

Answer

The slope of the function

Answer

The y-intercept of the function

Question 6

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

Accepted Answer

Downward-opening parabola

Answer

Upward-opening parabola

Answer

Positively sloped line

Answer

Negatively sloped line

Question 7

Identify the graph that accurately represents the linear function f(x) = 2x - 3.

Accepted Answer

Graph A: A line passing through (0, -3) with a slope of 2

Answer

Graph B: A line passing through (0, 3) with a slope of -2

Answer

Graph C: A parabola opening upward with its vertex at (0, -3)

Answer

Graph D: A line passing through (0, 0) with a slope of 3

Question 8

Identify the equation that represents a linear function:

Accepted Answer

y = 2x + 1

Answer

y = x^2 + 2

Answer

y = 1/x

Question 9

Which graph represents the linear function f(x) = 2x + 3?

Accepted Answer

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

Answer

A parabola with a vertex at (2, 3)

Answer

A circle with a radius of 3

Answer

An ellipse with a major axis of length 6

Question 10

Express the exponential equation 2^x = 8 in logarithmic form.

Accepted Answer

log₂(8) = x

Answer

8^log₂ = x

Answer

log(2) = 8x

Question 11

In the linear function f(x) = 2x + 3, what is the slope?

Accepted Answer

2

Answer

3

Answer

-2

Answer

The difference between the x and y intercepts

Question 12

In function notation, how do you determine the output value for a given input value?

Accepted Answer

Replace the input value directly into the function expression and calculate.

Answer

Plot the function and find the point corresponding to the input value.

Answer

Calculate the output value using the function's slope and y-intercept.

Answer

Additional information, like a table of values, is needed to find the output value.

Question 13

For the linear function f(x) = 2x + 1, the rate of change between any two points on its graph is:

Accepted Answer

2, the coefficient of x

Answer

Different for different points

Answer

1, the constant term

Answer

Undefined, as there is no variable

Question 14

To obtain a new function whose graph is shifted 2 units down and 1 unit to the right, which transformation should be applied to the linear function f(x) = 2x + 3?

Accepted Answer

Translate the graph 2 units down and 1 unit to the right by subtracting 2 from y and adding 1 to x.

Answer

Translate the graph 2 units down by subtracting 2 from y.

Answer

Translate the graph 1 unit to the right by adding 1 to x.

Answer

Translate the graph 2 units up and 1 unit to the left by adding 2 to y and subtracting 1 from x.

Question 15

For the function f(x) = sqrt(x + 5), what is the domain?

Accepted Answer

x ≥ -5

Answer

x ≤ -5

Answer

All real numbers

Question 16

Suppose you invest $500 in an account that compounds interest annually at a rate of 3%. How much money will be in the account after 10 years?

Accepted Answer

$566.05

Answer

$515.00

Answer

$530.00

Answer

$600.00

Question 17

Find the value of x in the logarithmic equation: log₂(8) = x.

Accepted Answer

3

Answer

16

Answer

4

Question 18

Find the equation of the linear function that goes through the point (2, 5) and is parallel to the line y = 3x - 1.

Accepted Answer

y = 3x + 11

Answer

y = 3x - 5

Answer

y = 2x + 9

Answer

y = x + 7

Question 19

Which of the following is NOT a property of a linear function?

Accepted Answer

Has a parabolic shape

Answer

Constant rate of change

Answer

Stretches or shrinks a graph

Answer

Intercepts the y-axis

Question 20

Identify the value of 'a' in the equation of a quadratic function: y = ax^2 + bx + c. Find the value of 'a' for the function y = -2x^2 + 5x - 3.

Accepted Answer

-2

Answer

-5

Answer

5

Answer

3

Question 21

Select the graph that represents an exponential function.

Accepted Answer

A curve that increases rapidly

Answer

A straight line

Answer

A parabola

Answer

A curve that decreases rapidly

Question 22

Determine the inverse of the function: f(x) = 2x - 3.

Accepted Answer

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

Answer

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

Answer

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

Answer

f^-1(x) does not exist

Question 23

Determine if the function f(x) = |x - 1| has an inverse function. Explain your reasoning.

Accepted Answer

No, it does not have an inverse function because it fails the horizontal line test.

Answer

Yes, it has an inverse function because it passes the horizontal line test.

Question 24

For the quadratic function f(x) = (x - 3)² - 1, identify its vertex and determine if it represents a minimum or maximum point.

Accepted Answer

Vertex: (3, -1); Minimum

Answer

Vertex: (3, -1); Maximum

Answer

Vertex: (-1, 3); Minimum

Answer

Vertex: (-1, 3); Maximum

Question 25

Find the solution to the system of linear equations:

2x + 3y = 7
3x - 2y = 1

Accepted Answer

x = 2, y = 1

Answer

x = 1, y = 2

Answer

x = 3, y = 2

Answer

x = 2, y = -1

Question 26

Which feature identifies an increasing function?

Accepted Answer

Its graph rises from left to right.

Answer

Its graph falls from left to right.

Answer

Its graph is a flat line.

Question 27

Find the equation of the linear function with a y-intercept of -3 that is perpendicular to the line y = 2x + 1.

Accepted Answer

y = -1/2x - 3

Answer

y = 2x - 6

Answer

y = -2x - 3

Answer

y = x - 3

Question 28

A radioactive substance decays exponentially over time. Initially, there are 100 grams of the substance. After 10 hours, only 50 grams remain. How many grams will remain after 20 hours?

Accepted Answer

25 grams

Answer

12.5 grams

Answer

50 grams

Question 29

Which of the following is not a function type covered in this unit?

Accepted Answer

Trigonometric

Answer

Exponential

Answer

Linear

Answer

Quadratic

Question 30

Identify the equation that represents a linear function:

Accepted Answer

y = 2x + 5

Answer

y = cos(x)

Answer

y = 3^x

Answer

y = x^2 - 4

Question 31

What is the domain of the function f(x) = (x - 2)/(x + 1)?

Accepted Answer

All real numbers except -1

Answer

All real numbers greater than 2

Answer

All negative real numbers

Answer

All positive real numbers

Question 32

Which graph represents the function y = -x^2 + 4?

Accepted Answer

A parabola opening downward

Answer

A parabola opening upward

Answer

A straight line with negative slope

Answer

A straight line with positive slope

Question 33

Solve for x in the equation: 3x - 5 = 10

Accepted Answer

x = 5

Answer

x = 15

Answer

x = -5

Question 34

Which of the following is the equation of a linear function?

Accepted Answer

y = mx + b, where m is the slope and b is the y-intercept

Answer

y = ax^2 + bx + c

Answer

x = y + b

Answer

y = e^(ax)

Question 35

Which of the following is the graph of a quadratic function?

Accepted Answer

A parabola

Answer

A line

Answer

A hyperbola

Answer

A circle

Question 36

Which of the following is the equation of an exponential function?

Accepted Answer

y = a^x, where a is the base

Answer

y = sin(x)

Answer

y = mx + b

Answer

y = ax^2 + bx + c

Question 37

What is the domain of the exponential function f(x) = 2^x?

Accepted Answer

All real numbers

Answer

Negative real numbers only

Answer

Positive real numbers only

Question 38

Which of the following is an application of functions in real life?

Accepted Answer

Modeling population growth

Answer

Solving quadratic equations

Answer

Finding the slope of a line

Answer

Calculating the area of a circle