Section 2.1 Homework

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Section 2.1 Homework

1. Complete the table.

$f (x) = 5 {(x - 6)}^{2}$

x	f(x)
-1
0
1
2
3

2. valuate the function at the indicated values. (If an answer is undefined, enter UNDEFINED.)

f(x) = x² − 3;

f(-3),

f(3),

f(0),

f (\frac{1}{2})

3. Evaluate the function at the indicated values. (If an answer is undefined, enter UNDEFINED.)

h (x) = \frac{x^{2} + 1}{2}

h(1) =

h(−1) =

h(a) =

h(−x) =

h(a − 1) =

\sqrt{x}

)

4. Evaluate the function at the indicated values. (If an answer is undefined, enter UNDEFINED.)

k(x) = −x² − 4x + 5;

k(0) =

k(4) =

k(−4) =

\sqrt{4}

) =

k(a + 4) =

k(−x) =

k(x²) =

5. Evaluate the piecewise defined function at the indicated values.

f (x) = \{\begin{cases} x^{2} & i f x < 0 \\ x + 4 & i f x \geq 0 \end{cases}

f(-3) =

f(-2) =

f(0) =

f(2) =

f(3) =

6. Use the function to evaluate the indicated expressions and simplify.

f(x) = 3x² + 2

f (x + 2) = f (x) + f (2) =

7. Find the net change in the value of the function between the given inputs.

f(x) = 3 − 6x; from 6 to 8

8. Find f(a),f(a + h),and the difference quotient

\frac{f (a + h) - f (a)}{h}

where h ≠ 0.

f (x) = 1 - 7 x

f (a) = f (a + h) = \frac{f (a + h) - f (a)}{h} =

9. Find f(a), f(a + h), and the difference quotient

\frac{f (a + h) - f (a)}{h}

where h ≠ 0

f (x) = 2 x^{2} + 4

f (a) = f (a + h) = \frac{f (a + h) - f (a)}{h} =

10. Find the domain and range of the function. (Enter your answers using interval notation.)

f(x) = 8x² + 1

domain =

range =

11. Find the domain of the function. (Enter your answer using interval notation.)

f (x) = \frac{1}{x - 4}

12. Find the domain of the function. (Enter your answer using interval notation.)

f (x) = \frac{x + 2}{x^{2} - 9}

13. Find the domain of the function. (Enter your answer using interval notation.)

g (t) = \sqrt{t^{2} + 4}

14. Find the domain of the function. (Enter your answer using interval notation.)

f (t) = \sqrt[5]{t - 5}

15. Find the domain of the function. (Enter your answer using interval notation.)

g (x) = \frac{\sqrt{7 + x}}{5 - x}

16. Find the domain of the function. (Enter your answer using interval notation.)

g (x) = \frac{\sqrt{x}}{8 x^{2} + 7 x - 1}

17. Find the domain of the function. (Enter your answer using interval notation.)

g (x) = \sqrt[4]{x^{2} - 2 x}

18. Find the domain of the function. (Enter your answer using interval notation.)

f (x) = \frac{x^{3}}{\sqrt{6 - x}}

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This question is taken from Math 110A – PreCalculus I » Fall 2021 » Homeworks

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