Question: 1 – Introduction to Functions
LEARNING OBJECTIVE: Evaluate a function for a given value.
If $f(x) = 2(x^2 + 5)$, then $f(-3) = \underline{\hspace{2cm}}$.
a.) 28
b.) -8
c.) -13
d.) 23
1. **State the problem:** We need to find the value of the function $f(x) = 2(x^2 + 5)$ when $x = -3$.
2. **Recall the formula:** The function is given by $$f(x) = 2(x^2 + 5).$$
3. **Substitute the value:** Replace $x$ with $-3$:
$$f(-3) = 2((-3)^2 + 5).$$
4. **Calculate inside the parentheses:**
$$(-3)^2 = 9,$$
so
$$f(-3) = 2(9 + 5).$$
5. **Simplify inside the parentheses:**
$$9 + 5 = 14,$$
thus
$$f(-3) = 2 \times 14.$$
6. **Multiply:**
$$f(-3) = 28.$$
7. **Conclusion:** The value of $f(-3)$ is $28$, so the correct answer is **a.) 28**.