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.

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

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

Watch the Step by Step Video Lesson  |  View the Written Solution

#2:

Instructions: graph each, state the domain and range.

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

Watch the Step by Step Video Lesson  |  View the Written Solution

#3:

Instructions: graph each, state the domain and range.

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

Watch the Step by Step Video Lesson  |  View the Written Solution

#4:

Instructions: graph each, state the domain and range.

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

Watch the Step by Step Video Lesson  |  View the Written Solution

#5:

Instructions: graph each, state the domain and range.

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

Watch the Step by Step Video Lesson  |  View the Written Solution

Written Solutions:

#1:

Solutions:

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

graph of y=x

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

graph of y=x^2

Watch the Step by Step Video Lesson

#2:

Solutions:

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

graph of y=x^3

Watch the Step by Step Video Lesson

#3:

Solutions:

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

graph of y=sqrt(x)

Watch the Step by Step Video Lesson

#4:

Solutions:

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

graph of y=cbrt(x)

Watch the Step by Step Video Lesson

#5:

Solutions:

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

graph of y=1/x

Watch the Step by Step Video Lesson