To solve the problem, we need to evaluate each function at the given input values. Let's go through each function step by step.
1. \( f(x) = -3x^2 - 3 \); find \( f(-2) \)
\[
f(-2) = -3(-2)^2 - 3 = -3(4) - 3 = -12 - 3 = -15
\]
Answer: \(-15\)
2. \( g(x) = x - 2 \); find \( g(-3) \)
\[
g(-3) = -3 - 2 = -5
\]
Answer: \(-5\)
3. \( h(a) = x + 4 \); find \( h(0) \)
\[
h(0) = 0 + 4 = 4
\]
Answer: \(4\)
4. \( f(t) = t^2 + 2 \); find \( f(-6) \)
\[
f(-6) = (-6)^2 + 2 = 36 + 2 = 38
\]
Answer: \(38\)
5. \( h(r) = r^3 + 5r^2 \); find \( h(2) \)
\[
h(2) = (2)^3 + 5(2)^2 = 8 + 5(4) = 8 + 20 = 28
\]
Answer: \(28\)
6. \( k(m) = m + 2 \); find \( k(-6) \)
\[
k(-6) = -6 + 2 = -4
\]
Answer: \(-4\)
7. \( p(x) = 2x - 2 \); find \( p(-5) \)
\[
p(-5) = 2(-5) - 2 = -10 - 2 = -12
\]
Answer: \(-12\)
8. \( h(x) = 3x^2 + 2 - 2x \); find \( h(-2) \)
\[
h(-2) = 3(-2)^2 + 2 - 2(-2) = 3(4) + 2 + 4 = 12 + 2 + 4 = 18
\]
Answer: \(18\)
9. \( g(a) = a^2 - 4 \); find \( g(10) \)
\[
g(10) = (10)^2 - 4 = 100 - 4 = 96
\]
Answer: \(96\)
10. \( p(x) = -x - 2 \); find \( p(-12) \)
\[
p(-12) = -(-12) - 2 = 12 - 2 = 10
\]
Answer: \(10\)
11. \( h(n) = n^3 - 4 \); find \( h(-3) \)
\[
h(-3) = (-3)^3 - 4 = -27 - 4 = -31
\]
Answer: \(-31\)
12. \( g(x) = 2x^2 - 4x + 7 \); find \( g(-4) \)
\[
g(-4) = 2(-4)^2 - 4(-4) + 7 = 2(16) + 16 + 7 = 32 + 16 + 7 = 55
\]
Answer: \(55\)
Final Answers:
\[
\boxed{-15, -5, 4, 38, 28, -4, -12, 18, 96, 10, -31, 55}
\]
Now, you can use these answers to follow the directions for each box and color your creations accordingly!
Parent Tip: Review the logic above to help your child master the concept of evaluating functions worksheet.