Unit Test Review - Linear Functions

1) Maddie's theater company put on a show and sold 500 tickets to the show. Floor seats cost $10 and balcony seats cost $5. Total ticket sales were $4500. Set up a system of equations and solve it to find the number of floor seats. Your answer should just be a number.

Your system of equations should be f + b = 500 and 10f + 5b = 4500.

Explanation

Your system of equations should be f + b = 500 and 10f + 5b = 4500.

Submit

2) Maddie's theater company put on a show and sold 500 tickets to the show. Floor seats cost $10 and balcony seats cost $5. Total ticket sales were $4500. Set up a system of equations and solve it to find the number of balcony seats. Your answer should just be a number.

Let's assume the number of floor seats sold is F and the number of balcony seats sold is B. The total number of tickets sold is 500, so we have the equation F + B = 500.

The price of each floor seat is $10, so the total revenue from floor seats is 10F. Similarly, the price of each balcony seat is $5, so the total revenue from balcony seats is 5B.

The total ticket sales were $4500, so we have the equation 10F + 5B = 4500.

By solving the system of equations, we can find the number of balcony seats, which is 100.

Explanation

Let's assume the number of floor seats sold is F and the number of balcony seats sold is B. The total number of tickets sold is 500, so we have the equation F + B = 500.

The price of each floor seat is $10, so the total revenue from floor seats is 10F. Similarly, the price of each balcony seat is $5, so the total revenue from balcony seats is 5B.

The total ticket sales were $4500, so we have the equation 10F + 5B = 4500.

By solving the system of equations, we can find the number of balcony seats, which is 100.

Submit

3) Given: f(x) = 3x - 2 Find f(0)

-2

-1

0

2

substitute in zero for x and evaluate the right side of the equation

Explanation

substitute in zero for x and evaluate the right side of the equation

4) Given: f(x) = 3x - 2 Find x if f(x) = 7

7

1

3

5

Start with 7= 3x - 2 and solve for x.

Explanation

Start with 7= 3x - 2 and solve for x.

5) Lia joins an art club that has an enrollment fee of $100 and costs $20 per month. Which equation correctly describes this situation with cost as a function of months?

C(m) = 100m + 20

C(m) = 20m + 100

M(c) = 100c + 20

M(c)= 20c + 100

The equation C(m) = 20m + 100 correctly describes the situation with cost as a function of months. The variable m represents the number of months, and the equation shows that the total cost C is determined by multiplying the number of months by 20 (the monthly cost) and adding the enrollment fee of $100.

Explanation

The equation C(m) = 20m + 100 correctly describes the situation with cost as a function of months. The variable m represents the number of months, and the equation shows that the total cost C is determined by multiplying the number of months by 20 (the monthly cost) and adding the enrollment fee of $100.

6) Translate the following statement into a coordinate point: h(3) = -1

(-1, 3)

(3, -1)

(1, 3)

(3, 1)

the quantity inside the parentheses is always the x value

Explanation

the quantity inside the parentheses is always the x value

7)

True or False: The relation shown above is a function.

True

False

It passes the vertical line test. There is really only one y value at x = 2 because of the "hole" in the graph.

Explanation

It passes the vertical line test. There is really only one y value at x = 2 because of the "hole" in the graph.

8)

Which equation correctly represents the linear function shown?

Y = 2x

Y = 2x + 1

Y = x + 1

Y = x

Since the graph goes through the origin you know the y-intercept is zero. Then you can see it goes up 2, and right 1, to the point (1, 2) giving you a slope of 2/1 which is equal to 2.

Explanation

Since the graph goes through the origin you know the y-intercept is zero. Then you can see it goes up 2, and right 1, to the point (1, 2) giving you a slope of 2/1 which is equal to 2.

9)

What is the value of x when f(x) = 3?

1

2

3

Both a and c are correct

The value of x when f(x) = 3 can be either 1 or 3. This is because "Both a and c are correct" implies that both options 1 and 3 are correct answers. Therefore, either 1 or 3 can be the value of x that satisfies the equation f(x) = 3.

Explanation

The value of x when f(x) = 3 can be either 1 or 3. This is because "Both a and c are correct" implies that both options 1 and 3 are correct answers. Therefore, either 1 or 3 can be the value of x that satisfies the equation f(x) = 3.

10)

What is f(1)?

1

2

3

4

not-available-via-ai

Explanation

not-available-via-ai

11)

What is the domain of the relation shown above?

[1, 3]

(1, 3)

[1, 2) U (2, 3]

{1} U (2, 3]

The domain of a relation refers to the set of all possible input values or x-values. In this case, the relation is shown to have values ranging from 1 to 3, inclusive of both endpoints. Therefore, the correct answer is [1, 3].

Explanation

The domain of a relation refers to the set of all possible input values or x-values. In this case, the relation is shown to have values ranging from 1 to 3, inclusive of both endpoints. Therefore, the correct answer is [1, 3].

12) Find an equation of a linear function given g(0) = 5 and g(-2) = 4.

G(x) = -2x + 5

G(x) = 4x

Take the points (0, 5) and (-2, 4) and find the slope. Then you can substitute into the point-slope formula using one of the points OR the slope-intercept formula since you can see the first point is the y-intercept.

Explanation

Take the points (0, 5) and (-2, 4) and find the slope. Then you can substitute into the point-slope formula using one of the points OR the slope-intercept formula since you can see the first point is the y-intercept.