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:

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

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

#2:

Solutions:

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

#3:

Solutions:

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

#4:

Solutions:

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

#5:

Solutions:

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