Section 2.1 Functions and their graphs

1. Let h be the function defined by the equation below.

$h\left(x\right)=x^3–x^2+x+8$

Find the following:

h(-7)=

h(0)-=

h(a)=

h(-a)=

2. Let g be the function defined by the equation below.

$g\left(u\right)={(3u–2)}^{3/2}$

Find the following:

g(1)=

g(2)=

$g\left(\frac{38}{3}\right)=$

g(u+1)=

3.  Refer to the graph of the function f in the following figure.

a. Find f(0)

b. Find the value of x for which f(x) = 3 and f(x)=0

c. Find the domain of f

d. Find the range of f

4. Refer to the graph of the function f in the following figure.

(a) Find the value of f(9)

b. Find the values of x corresponding to the point(s) on the graph of f located at a height of 5 units above the x-axis.

c. Find the point on the x-axis at which the graph of f crosses it.

d. Find the domain and range of f. (Enter your answers using interval notation.)

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

$f\left(x\right) = 3=x^2$

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

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

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

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

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

$f\left(x\right)=\frac{1}{x^2+5x–36}$

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

$g\left(x\right)=4{(x–6)}^{5/2}$

12. Use the vertical-line test to determine whether the graph represents y as a function of x.

13.  Use the vertical-line test to determine whether the graph represents y as a function of x.