The image presents five function-related problems. We will solve each problem separately. Question 1 asks if a given relationship is a function. Question 2 asks for a description of the graph of a plane's height over time. Question 3 asks to graph the function $f(x) = x^2$ and to explain if it is a linear function. Question 4 asks to write a linear function $y = mx + b$ that contains the points $(4, 9)$ and $(-10, 16)$. Question 5 involves a word problem about Cooper's gift card balance and the number of games he can buy. We need to write a function, graph it, and determine the maximum number of games.

1. Problem Description

The image presents five function-related problems. We will solve each problem separately.

Question 1 asks if a given relationship is a function.

Question 2 asks for a description of the graph of a plane's height over time.

Question 3 asks to graph the function $f(x) = x^2$ and to explain if it is a linear function.

Question 4 asks to write a linear function $y = mx + b$ that contains the points $(4, 9)$ and $(-10, 16)$.

Question 5 involves a word problem about Cooper's gift card balance and the number of games he can buy. We need to write a function, graph it, and determine the maximum number of games.

2. Solution Steps

Question 1: Is this relationship a function? Explain why or why not.

The relation is: -8 -> 5, -2 -> q, 0 -> H, 4 -> H, 10 ->

1

8. A relation is a function if each input has only one output. In this case, each input has exactly one output.

Therefore, this is a function.

Question 2: Describe the graph of a plane's height over time.

The graph shows the altitude of a plane in feet over time in minutes.

The plane's altitude increases linearly for a period of time. Then, the altitude remains constant for a period of time. After that, the altitude decreases linearly until it reaches zero.

Question 3: Graph the function $f(x) = x^2$. Is it a linear function? Explain.

To graph the function, we can pick a few values for $x$ and find the corresponding $f(x)$ values.

x = -2, f(x) = 4

x = -1, f(x) = 1

x = 0, f(x) = 0

x = 1, f(x) = 1

x = 2, f(x) = 4

The graph of $f(x) = x^2$ is a parabola. A linear function has the form $f(x) = mx + b$, where $m$ and $b$ are constants. The graph of a linear function is a straight line. Since the graph of $f(x) = x^2$ is not a straight line, it is not a linear function.

Question 4: Write a function in the form $y = mx + b$ for the line that contains the points $(4, 9)$ and $(-10, 16)$.

First, we need to find the slope $m$.

$m = \frac{y_2 - y_1}{x_2 - x_1}$

$m = \frac{16 - 9}{-10 - 4} = \frac{7}{-14} = -\frac{1}{2}$

Now we have $y = -\frac{1}{2}x + b$. We can plug in one of the points to solve for $b$.

Using the point (4, 9):

$9 = -\frac{1}{2}(4) + b$

$9 = -2 + b$

$b = 11$

So the equation is $y = -\frac{1}{2}x + 11$.

Question 5: Cooper has an $80 Apple gift card. He plans to buy one new game each week for$7.

5

0. Write a function to describe the relationship.

Let $y$ be the amount of gift card left, and $x$ be the number of games he buys.

Then $y = 80 - 7.50x$

Graph the Function:

To graph, we can find two points. When x = 0, y =

8

0. When y = 0, $0 = 80 - 7.50x$, so $7.50x = 80$, and $x = \frac{80}{7.50} = \frac{800}{75} = \frac{32}{3} \approx 10.67$

How many games can he buy before he runs out of money?

Since he can only buy whole games, he can buy 10 games before he runs out of money. After buying 10 games, he'll have $80 - 10(7.50) = 80 - 75 =$5 left, which is not enough to buy another game.

3. Final Answer

Question 1: Yes, it is a function because each input has only one output.

Question 2: The plane's altitude increases linearly, remains constant, and then decreases linearly.

Question 3: The graph of $f(x) = x^2$ is a parabola. No, it is not a linear function because its graph is not a straight line.

Question 4: $y = -\frac{1}{2}x + 11$

Question 5:

Function: $y = 80 - 7.50x$

He can buy 10 games before he runs out of money.