5. given $f(x) = 3x - 5$, which statement is true?
a) $f(0) = 0$
b) $f(3) = 4$
c) $f(4) = 3$
d) $f(5) = 0$
6. the height of a ball hit into the air is modeled by the equation $h = -16t^2 + 48t$, where $h$ represents the height, in feet, and $t$ represents the number of seconds that have passed since the ball was hit. what is the height of the ball after 2 seconds?
7. the function $g(x)$ is defined as $g(x) = -2x^2 + 3x$. the value of $g(-3)$ is:
8. given $f(x) = 2x + 3$, find the value of $x$ when:
a) $f(x) = 1$
b) $f(x) = 23$
9. the graph of $y = f(x)$ is shown below.
which point could be used to find $f(2)$?
graph of a coordinate plane with points a, b, c, d

Question

Accepted Answer

### Question 5
# Explanation:
## Step1: Check option a: Calculate $ f(0) $
To find $ f(0) $, substitute $ x = 0 $ into $ f(x)=3x - 5 $.
$ f(0)=3(0)-5=-5
eq0 $, so option a is false.
## Step2: Check option b: Calculate $ f(3) $
Substitute $ x = 3 $ into $ f(x)=3x - 5 $.
$ f(3)=3(3)-5 = 9 - 5=4 $, so option b is true.
## Step3: Check option c: Calculate $ f(4) $
Substitute $ x = 4 $ into $ f(x)=3x - 5 $.
$ f(4)=3(4)-5=12 - 5 = 7
eq3 $, so option c is false.
## Step4: Check option d: Calculate $ f(5) $
Substitute $ x = 5 $ into $ f(x)=3x - 5 $.
$ f(5)=3(5)-5=15 - 5 = 10
eq0 $, so option d is false.
# Answer: b) $ f(3)=4 $

### Question 6
# Explanation:
## Step1: Substitute $ t = 2 $ into the equation $ h=-16t^{2}+48t $
We need to find the height $ h $ when $ t = 2 $. So we substitute $ t = 2 $ into the given formula.
$ h=-16(2)^{2}+48(2) $
## Step2: Calculate the value of $ h $
First, calculate $ (2)^{2}=4 $, then $ -16\times4=-64 $ and $ 48\times2 = 96 $. Then add these two results: $ h=-64 + 96=32 $.
# Answer: The height of the ball after 2 seconds is 32 feet.

### Question 7
# Explanation:
## Step1: Substitute $ x=-3 $ into $ g(x)=-2x^{2}+3x $
To find $ g(-3) $, we replace $ x $ with $ -3 $ in the function $ g(x) $.
$ g(-3)=-2(-3)^{2}+3(-3) $
## Step2: Calculate the value of $ g(-3) $
First, calculate $ (-3)^{2}=9 $, then $ -2\times9=-18 $ and $ 3\times(-3)=-9 $. Then add these two results: $ g(-3)=-18-9=-27 $.
# Answer: $ g(-3)=-27 $

### Question 8
#### Part (a)
# Explanation:
## Step1: Set up the equation
Given $ f(x)=2x + 3 $ and $ f(x)=1 $, we set $ 2x+3 = 1 $.
## Step2: Solve for $ x $
Subtract 3 from both sides: $ 2x=1 - 3=-2 $. Then divide both sides by 2: $ x=\frac{-2}{2}=-1 $.
# Answer: $ x=-1 $

#### Part (b)
# Explanation:
## Step1: Set up the equation
Given $ f(x)=2x + 3 $ and $ f(x)=23 $, we set $ 2x+3 = 23 $.
## Step2: Solve for $ x $
Subtract 3 from both sides: $ 2x=23 - 3 = 20 $. Then divide both sides by 2: $ x=\frac{20}{2}=10 $.
# Answer: $ x = 10 $

### Question 9
# Explanation:
To find $ f(2) $, we need to find the point on the graph of $ y = f(x) $ where the $ x $-coordinate is 2. In the coordinate plane, a point is represented as $ (x,y) $, and for the function $ y = f(x) $, $ y=f(x) $. So to find $ f(2) $, we need a point with $ x = 2 $, i.e., the point $ (2,y) $ where $ y=f(2) $. Among the points A, B, C, D, we need to identify the point with $ x = 2 $. (Assuming from the graph, the point with $ x = 2 $ on the x - axis and its corresponding y - value is the point to find $ f(2) $. If we assume the points are labeled such that the x - coordinate of the point is 2, then the point $ (2,y) $ will give $ f(2)=y $.)
# Answer: The point with $ x = 2 $ (i.e., the point where the x - coordinate is 2) on the graph of $ y = f(x) $ can be used to find $ f(2) $. If we consider the labeled points, we need to look for the point with $ x = 2 $. (Since the graph is not fully described in terms of coordinates of A, B, C, D, but in general, the point $ (2,f(2)) $ is used to find $ f(2) $)

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QUESTION IMAGE

Question

Explanation:

Question 5

Step1: Check option a: Calculate \( f(0) \)

Step2: Check option b: Calculate \( f(3) \)

Step3: Check option c: Calculate \( f(4) \)

Step4: Check option d: Calculate \( f(5) \)

Step1: Substitute \( t = 2 \) into the equation \( h=-16t^{2}+48t \)

Step2: Calculate the value of \( h \)

Step1: Substitute \( x=-3 \) into \( g(x)=-2x^{2}+3x \)

Step2: Calculate the value of \( g(-3) \)

Answer:

Question 6