Scroll to Top

Virtual Math Learning Center

Virtual Math Learning Center Texas A&M University Virtual Math Learning Center

Section 1.4 – Functions

  • The definition of a function 
  • Terminology for functions including domain, range, independent variable, and dependent variable
  • Function notation
  • Evaluating functions
  • Piecewise functions
  • Finding the domain of a function

Exercises

Directions: You should try to solve each problem first, and then click "Reveal Answer" to check your answer. You can click "Watch Video" if you need help with a problem.

1. Determine whether each equation represents \(y\) as a function of \(x\)

  1. \(y-1=4x\)
  2. \(x=|2y-1|\)
  3. \(2x^3+y^2=4\)
  4. \(y^3-4x=6\)

  1. Yes
  2. No
  3. No
  4. Yes

If you would like to see more videos on this topic, click the following link and check the related videos.

2. Consider the function \[h(x)=\left\{ \begin{array}{cc}-2x+4 & \textrm{, if } x \leq -1 \\(x-2)^2 & \textrm{, if } x >-1\\ \end{array} \right. \] Find \(h(-2)\), \(h(-1)\), and \(h(2).\)

\(h(-2)=8\)
\(h(-1)=6\) 
\(h(2)=0\)

If you would like to see more videos on this topic, click the following link and check the related videos.

3. Find the domain of the following functions.

  1. \(f(x)=-3x^2+5\)
  2. \(g(x)=\sqrt{4-3x}\)
  3. \(p(x)=\cfrac{x-1}{\sqrt{x+4}}\)
  4. \(q(x)=\sqrt[3]{4-3x}\)

  1. D: \( (-\infty, \infty)\)
  2. D: \(\left(-\infty, \dfrac{4}{3}\right]\)
  3. D: \((-4, \infty)\)
  4. D: \((-\infty, \infty)\)

If you would like to see more videos on this topic, click the following link and check the related videos.

4. Find the domain of the following expressions.

  1. \(​\displaystyle \frac{x^2-5x+6}{x^2+2x-8}\)
  2. \(\displaystyle \frac{1}{\sqrt{x-7}}\)

  1. Domain: \((-\infty,-4)\cup(-4,2)\cup(2,\infty)\)
  2. Domain: \((7,\infty)\)

If you would like to see more videos on this topic, click the following link and check the related videos.

Change the section

Prev Section Next Section Return to Course