Function Notation worksheets - Free Printable

To solve the given problems, we need to evaluate each function at the specified value of the variable. Let's go through each problem step by step.

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Problem 1: \( f(x) = 4x - 7 \), Find: \( f(5) \)

1. Substitute \( x = 5 \) into the function \( f(x) = 4x - 7 \):
\[
f(5) = 4(5) - 7
\]
2. Perform the multiplication:
\[
4(5) = 20
\]
3. Subtract 7:
\[
20 - 7 = 13
\]

Answer:
\[
\boxed{13}
\]

---

Problem 2: \( y(x) = 3x^2 + 2x + 1 \), Find: \( y(2) \)

1. Substitute \( x = 2 \) into the function \( y(x) = 3x^2 + 2x + 1 \):
\[
y(2) = 3(2)^2 + 2(2) + 1
\]
2. Calculate \( (2)^2 \):
\[
(2)^2 = 4
\]
3. Multiply by 3:
\[
3(4) = 12
\]
4. Multiply \( 2(2) \):
\[
2(2) = 4
\]
5. Add all terms together:
\[
12 + 4 + 1 = 17
\]

Answer:
\[
\boxed{17}
\]

---

Problem 3: \( g(t) = 2t - 4 \), Find: \( g(3) \)

1. Substitute \( t = 3 \) into the function \( g(t) = 2t - 4 \):
\[
g(3) = 2(3) - 4
\]
2. Perform the multiplication:
\[
2(3) = 6
\]
3. Subtract 4:
\[
6 - 4 = 2
\]

Answer:
\[
\boxed{2}
\]

---

Problem 4: \( h(u) = u^2 - 5 \), Find: \( h(2) \)

1. Substitute \( u = 2 \) into the function \( h(u) = u^2 - 5 \):
\[
h(2) = (2)^2 - 5
\]
2. Calculate \( (2)^2 \):
\[
(2)^2 = 4
\]
3. Subtract 5:
\[
4 - 5 = -1
\]

Answer:
\[
\boxed{-1}
\]

---

Problem 5: \( f(x) = 10x + 5 \), Find: \( f(-1) \)

1. Substitute \( x = -1 \) into the function \( f(x) = 10x + 5 \):
\[
f(-1) = 10(-1) + 5
\]
2. Perform the multiplication:
\[
10(-1) = -10
\]
3. Add 5:
\[
-10 + 5 = -5
\]

Answer:
\[
\boxed{-5}
\]

---

Problem 6: \( y(x) = x^3 - 5x \), Find: \( y(3) \)

1. Substitute \( x = 3 \) into the function \( y(x) = x^3 - 5x \):
\[
y(3) = (3)^3 - 5(3)
\]
2. Calculate \( (3)^3 \):
\[
(3)^3 = 27
\]
3. Multiply \( 5(3) \):
\[
5(3) = 15
\]
4. Subtract:
\[
27 - 15 = 12
\]

Answer:
\[
\boxed{12}
\]

---

Problem 7: \( g(t) = 4t^2 - 4t \), Find: \( g(1) \)

1. Substitute \( t = 1 \) into the function \( g(t) = 4t^2 - 4t \):
\[
g(1) = 4(1)^2 - 4(1)
\]
2. Calculate \( (1)^2 \):
\[
(1)^2 = 1
\]
3. Multiply:
\[
4(1) = 4 \quad \text{and} \quad 4(1) = 4
\]
4. Subtract:
\[
4 - 4 = 0
\]

Answer:
\[
\boxed{0}
\]

---

Problem 8: \( h(x) = 5(x - 3) \), Find: \( h(2) \)

1. Substitute \( x = 2 \) into the function \( h(x) = 5(x - 3) \):
\[
h(2) = 5(2 - 3)
\]
2. Simplify inside the parentheses:
\[
2 - 3 = -1
\]
3. Multiply:
\[
5(-1) = -5
\]

Answer:
\[
\boxed{-5}
\]

---

Problem 9: \( y(x) = 2x^2 + 2x + 1 \), Find: \( y(1) \)

1. Substitute \( x = 1 \) into the function \( y(x) = 2x^2 + 2x + 1 \):
\[
y(1) = 2(1)^2 + 2(1) + 1
\]
2. Calculate \( (1)^2 \):
\[
(1)^2 = 1
\]
3. Multiply:
\[
2(1) = 2 \quad \text{and} \quad 2(1) = 2
\]
4. Add all terms:
\[
2 + 2 + 1 = 5
\]

Answer:
\[
\boxed{5}
\]

---

Problem 10: \( f(x) = 4x - 6 \), Find: \( f(10) \)

1. Substitute \( x = 10 \) into the function \( f(x) = 4x - 6 \):
\[
f(10) = 4(10) - 6
\]
2. Perform the multiplication:
\[
4(10) = 40
\]
3. Subtract 6:
\[
40 - 6 = 34
\]

Answer:
\[
\boxed{34}
\]

---

Problem 11: \( h(z) = z^3 \), Find: \( h(-2) \)

1. Substitute \( z = -2 \) into the function \( h(z) = z^3 \):
\[
h(-2) = (-2)^3
\]
2. Calculate \( (-2)^3 \):
\[
(-2)^3 = -8
\]

Answer:
\[
\boxed{-8}
\]

---

Problem 12: \( m(u) = 10u - u^2 \), Find: \( m(2) \)

1. Substitute \( u = 2 \) into the function \( m(u) = 10u - u^2 \):
\[
m(2) = 10(2) - (2)^2
\]
2. Perform the multiplications:
\[
10(2) = 20 \quad \text{and} \quad (2)^2 = 4
\]
3. Subtract:
\[
20 - 4 = 16
\]

Answer:
\[
\boxed{16}
\]

---

Problem 13: \( f(x) = 10x - 9 \), Find: \( f(4) \)

1. Substitute \( x = 4 \) into the function \( f(x) = 10x - 9 \):
\[
f(4) = 10(4) - 9
\]
2. Perform the multiplication:
\[
10(4) = 40
\]
3. Subtract 9:
\[
40 - 9 = 31
\]

Answer:
\[
\boxed{31}
\]

---

Problem 14: \( h(x) = 4x^2 - 5x + 1 \), Find: \( h(2) \)

1. Substitute \( x = 2 \) into the function \( h(x) = 4x^2 - 5x + 1 \):
\[
h(2) = 4(2)^2 - 5(2) + 1
\]
2. Calculate \( (2)^2 \):
\[
(2)^2 = 4
\]
3. Multiply:
\[
4(4) = 16 \quad \text{and} \quad 5(2) = 10
\]
4. Subtract and add:
\[
16 - 10 + 1 = 7
\]

Answer:
\[
\boxed{7}
\]

---

Final Answers:

\[
\boxed{
\begin{aligned}
1. & \ 13 \\
2. & \ 17 \\
3. & \ 2 \\
4. & \ -1 \\
5. & \ -5 \\
6. & \ 12 \\
7. & \ 0 \\
8. & \ -5 \\
9. & \ 5 \\
10. & \ 34 \\
11. & \ -8 \\
12. & \ 16 \\
13. & \ 31 \\
14. & \ 7
\end{aligned}
}
\]