About Graphs of Functions:

We need to be able to identify the graphs of basic functions. The identity function, y = x, the squaring function, y = x2, the cubing function, y = x3, the square root function, y = sqrt(x), the cube root function, y = cbrt(x), and the reciprocal function, y = 1/x. We also need to be familiar with the domain and range for each function.


Test Objectives
  • Demonstrate the ability to sketch the graph of a function
  • Demonstrate the ability to find the domain of a function based on its graph
  • Demonstrate the ability to find the range of a function based on its graph
Graphs of Functions Practice Test:

#1:

Instructions: graph each, state the domain and range.

$$a)\hspace{.2em}f(x)=x$$

$$b)\hspace{.2em}f(x)=x^2$$


#2:

Instructions: graph each, state the domain and range.

$$a)\hspace{.2em}f(x)=x^3$$


#3:

Instructions: graph each, state the domain and range.

$$a)\hspace{.2em}f(x)=\sqrt{x}$$


#4:

Instructions: graph each, state the domain and range.

$$a)\hspace{.2em}f(x)=\sqrt[3]{x}$$


#5:

Instructions: graph each, state the domain and range.

$$a)\hspace{.2em}f(x)=\frac{1}{x}$$


Written Solutions:

#1:

Solutions:

$$a)\hspace{.2em}$$ $$\text{Domain}: (-\infty, \infty)$$ $$\text{Range}: (-\infty, \infty)$$

graph of y=x

$$b)\hspace{.2em}$$ $$\text{Domain}: (-\infty, \infty)$$ $$\text{Range}: [0, \infty)$$

graph of y=x^2

#2:

Solutions:

$$a)\hspace{.2em}$$ $$\text{Domain}: (-\infty, \infty)$$ $$\text{Range}: (-\infty, \infty)$$

graph of y=x^3

#3:

Solutions:

$$a)\hspace{.2em}$$ $$\text{Domain}: [0, \infty)$$ $$\text{Range}: [0, \infty)$$

graph of y=sqrt(x)

#4:

Solutions:

$$a)\hspace{.2em}$$ $$\text{Domain}: (-\infty, \infty)$$ $$\text{Range}: (-\infty, \infty)$$

graph of y=cbrt(x)

#5:

Solutions:

$$a)\hspace{.2em}$$ $$\text{Domain}: (-\infty, 0) ∪ (0, \infty)$$ $$\text{Range}: (-\infty, 0) ∪ (0, \infty)$$

graph of y=1/x