Question

Question 1
A)(3 points)
Use the function f(x)=2x3−3x2+7
to complete the exercises.

f(−1)=


f(1)=


f(2)=


Question 2
A)
The function f(x)=12x+32
is used to complete this table.

x f(x)
-1 1
0 32
1 2
2 52
Which statements are true given the function? Select the two that apply.

(2 points)
Responses

f(1)=−1
f of 1 is equal to negative 1

f(0)=32
f of 0 is equal to 3 halves

f(2)=1
f of 2 is equal to 1

f(−12)=−2
f of open paren negative 1 half close paren is equal to negative 2

f(4)=72
f of 4 is equal to 7 halves
Question 3
A)The function p(x)=−2(x−9)2+100
is used to determine the profit on t-shirts sold for x dollars. What would the profit from sales be if the price of the t-shirts were $15 each?(1 point)
Responses

$244
$244

$172
$172

$15
$15

$28
$28
Question 4
A)
Use the graph to answer fill in the blanks.



(2 points)
f(4)=


If g(x)=30
, then x=

.

Answer 1

### Question 1

**A)** Use the function \( f(x) = 2x^3 - 3x^2 + 7 \) to complete the exercises.

1. **\( f(-1) \)**:
\[
f(-1) = 2(-1)^3 - 3(-1)^2 + 7 = 2(-1) - 3(1) + 7 = -2 - 3 + 7 = 2
\]

2. **\( f(1) \)**:
\[
f(1) = 2(1)^3 - 3(1)^2 + 7 = 2(1) - 3(1) + 7 = 2 - 3 + 7 = 6
\]

3. **\( f(2) \)**:
\[
f(2) = 2(2)^3 - 3(2)^2 + 7 = 2(8) - 3(4) + 7 = 16 - 12 + 7 = 11
\]

### Final Answers for Question 1:
- \( f(-1) = 2 \)
- \( f(1) = 6 \)
- \( f(2) = 11 \)

---

### Question 2

**A)** The function \( f(x) = 12x + 32 \) is used to complete this table.

Check the statements:

1. **\( f(1) = -1 \)**:
- \( f(1) = 12(1) + 32 = 12 + 32 = 44 \) (False)

2. **\( f(0) = 32 \)**:
- \( f(0) = 12(0) + 32 = 0 + 32 = 32 \) (True)

3. **\( f(2) = 1 \)**:
- \( f(2) = 12(2) + 32 = 24 + 32 = 56 \) (False)

4. **\( f(-1) = -2 \)**:
- \( f(-1) = 12(-1) + 32 = -12 + 32 = 20 \) (False)

5. **\( f(4) = 72 \)**:
- \( f(4) = 12(4) + 32 = 48 + 32 = 80 \) (False)

### Final Answers for Question 2:
- The true statement is: \( f(0) = 32 \)

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### Question 3

**A)** The function \( p(x) = -2(x - 9)^2 + 100 \) is used to determine the profit on t-shirts sold for \( x \) dollars. What would the profit from sales be if the price of the t-shirts were $15 each?

Substituting \( x = 15 \) into \( p(x) \):

\[
p(15) = -2(15 - 9)^2 + 100 = -2(6)^2 + 100 = -2(36) + 100 = -72 + 100 = 28
\]

### Final Answer for Question 3:
- Profit = $28

---

### Question 4

**A)** Use the graph to answer fill in the blanks. (Since the graph is not available, I can't provide exact values here.)

1. **\( f(4) = \)**:
(You would need to determine the value from the graph.)

2. **If \( g(x) = 30 \), then \( x = \)**:
(You would also need to find this value from the graph where \( g(x) = 30 \).)

Please refer to the graph for the exact answers in Question 4.