# 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.

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

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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)$$.

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

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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. $$q(x)=\sqrt[3]{4-3x}$$​

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

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

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

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