Section 1.4 – Functions

Section Details.

• 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

Practice Problems

Directions. The following are review problems for the section. We recommend you work the problems yourself, and then click "Answer" to check your answer. If you do not understand a problem, you can click "Video" to learn how to solve it. 

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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. \(y^3-4x=6\)
      Answer

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

      Video

      
      To see the full video page and find related videos, click the following link.
      WIR2 20B M150 V8

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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 \(h(2)\).
   Answer

   \(h(-2)=8\)
   \(h(-1)=6\) 
   \(h(2)=0\)

   Video

   
   To see the full video page and find related videos, click the following link.
   WIR2 20B M150 V9

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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. \(q(x)=\sqrt[3]{4-3x}\)​
      Answer

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

      Video

      
      To see the full video page and find related videos, click the following link.
      WIR2 20B M150 V10

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4. ​Find the domain of the following expressions.
   1. \(​\displaystyle \frac{x^2-5x+6}{x^2+2x-8}\)
   2. \(\displaystyle \frac{1}{\sqrt{x-7}}\)
      Answer

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

      Video

      
      To see the full video page and find related videos, click the following link.
      WIR8 20B M150 V03

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