2. Evaluate the function for the given value. a) $$ f(x)=2 x^{3}-5 x^{2}-16 x \cdot x=1 $$ в) $$ p(x)=-x^{5}+1 x^{4}+7+x+3 $$ c) $$ h(x) $$ $$ -3 x^{1}+2 x^{3}-12 x-6 ; x=-2 $$ d) $$ f(x)=7 x^{\prime}-10 x^{2}-11 x-26 $$

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Sure, let's evaluate each function at the given values step by step.

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### **Problem 2: Evaluate the function for the given value.**

#### **a) $$ f(x) = 2x^{3} - 5x^{2} - 16x $$ at $$ x = 1 $$**

**Solution:**

Plug $$ x = 1 $$ into the function:

$$
f(1) = 2(1)^3 - 5(1)^2 - 16(1)
$$

Calculate each term:

$$
2(1)^3 = 2 \times 1 = 2
$$
$$
-5(1)^2 = -5 \times 1 = -5
$$
$$
-16(1) = -16
$$

Add them together:

$$
f(1) = 2 - 5 - 16 = -19
$$

**Answer:** $$ f(1) = -19 $$

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#### **b) $$ p(x) = -x^{5} + x^{4} + 7 + x + 3 $$ at $$ x = 1 $$**

*(Assuming you want to evaluate at $$ x = 1 $$ since no specific value was provided.)*

**Solution:**

Plug $$ x = 1 $$ into the function:

$$
p(1) = -(1)^5 + (1)^4 + 7 + 1 + 3
$$

Calculate each term:

$$
-(1)^5 = -1
$$
$$
(1)^4 = 1
$$
$$
7 = 7
$$
$$
1 = 1
$$
$$
3 = 3
$$

Add them together:

$$
p(1) = -1 + 1 + 7 + 1 + 3 = 11
$$

**Answer:** $$ p(1) = 11 $$

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#### **c) $$ h(x) = -3x + 2x^{3} - 12x - 6 $$ at $$ x = -2 $$**

**Solution:**

Plug $$ x = -2 $$ into the function:

$$
h(-2) = -3(-2) + 2(-2)^3 - 12(-2) - 6
$$

Calculate each term:

$$
-3(-2) = 6
$$
$$
2(-2)^3 = 2(-8) = -16
$$
$$
-12(-2) = 24
$$
$$
-6 = -6
$$

Add them together:

$$
h(-2) = 6 - 16 + 24 - 6 = 8
$$

**Answer:** $$ h(-2) = 8 $$

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#### **d) $$ f(x) = 7x - 10x^{2} - 11x - 26 $$ at $$ x = \text{Given Value} $$**

*(The problem statement does not provide a value for $$ x $$ in part d. I'll assume you want to evaluate it at $$ x = 1 $$. If you have a different value, please provide it.)*

**Solution:**

Assuming $$ x = 1 $$:

$$
f(1) = 7(1) - 10(1)^2 - 11(1) - 26
$$

Calculate each term:

$$
7(1) = 7
$$
$$
-10(1)^2 = -10
$$
$$
-11(1) = -11
$$
$$
-26 = -26
$$

Add them together:

$$
f(1) = 7 - 10 - 11 - 26 = -40
$$

**Answer:** $$ f(1) = -40 $$

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**Summary of Evaluations:**

- **a)** $$ f(1) = -19 $$
- **b)** $$ p(1) = 11 $$
- **c)** $$ h(-2) = 8 $$
- **d)** $$ f(1) = -40 $$ *(Assuming $$ x = 1 $$)*

If you intended to evaluate part **b)** or **d)** at different values of $$ x $$, please provide those values and I'd be happy to help!
**Evaluations:** - **a)** $$ f(1) = -19 $$ - **b)** $$ p(1) = 11 $$ - **c)** $$ h(-2) = 8 $$ - **d)** $$ f(1) = -40 $$

2. Evaluate the function for the given value. a) \( f(x)=2 x^{3}-5 x^{2}-16 x \cdot x=1 \) в) \( p(x)=-x^{5}+1 x^{4}+7+x+3 \) c) \( h(x) \) \( -3 x^{1}+2 x^{3}-12 x-6 ; x=-2 \) d) \( f(x)=7 x^{\prime}-10 x^{2}-11 x-26 \)

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