Review of Pre-Calculus Formulas from Geometry [latex]A=\text{area},[/latex][latex]V=\text{Volume},\text{ and }[/latex][latex]S=\text{lateral surface area}[/latex]

Let [latex]f\left(x\right)=\frac{1}{x}.[/latex] Find a number[latex]\text{ }c\text{ }[/latex]such that the average rate of change of the function[latex]\text{ }f\text{ }[/latex]on the interval[latex]\text{ }\left(1,c\right)\text{ }[/latex]is[latex]\text{ }-\frac{1}{4}.[/latex]

Given the function [latex]f\left(x\right)=\sqrt[\leftroot{1}\uproot{2} ]{x},[/latex] graph the original function [latex]f\left(x\right)[/latex] and the transformation [latex]g\left(x\right)=f\left(x+2\right)[/latex] on the same axes.

Many quadratic equations with a leading coefficient other than 1 can be solved by factoring using the grouping method. Another method for solving quadratics is the square root property. The variable is squared.

By the definition of an ellipse, [latex]{d}_{1}+{d}_{2}[/latex] is constant for any point [latex]\left(x,y\right)[/latex] on the ellipse. We know that the sum of these distances is [latex]2a[/latex] for the vertex [latex]\left(a,0\right)[/latex].

Module 1: Introduction to Functions Functions and Function Notation; Domain and Range; Rates of Change and Behavior of Graphs; Composition of Functions; Transformation of Functions; Absolute Value Functions; Inverse Functions; Problem Set 1: Functions and Function Notation; Problem Set 2: Domain and Range

Example 1: WRITE THE STANDARD FORM Equation OF A CIRCLE. Write the standard form of a circle with radius [latex]3[/latex] and center [latex](0,0)[/latex].

Example 1: Identifying Discontinuities. Identify all discontinuities for the following functions as either a jump or a removable discontinuity. [latex]f\left(x\right)=\frac{{x}^{2}-2x - 15}{x - 5}[/latex] [latex]g\left(x\right)=\begin{cases}x+1, \hfill& x; 2 \\ -x, \hfill& x\geq2\end{cases}[/latex]

For the following exercises, evaluate the function[latex]\text{ }f\text{ }[/latex]at the values[latex]f\left(-2\right),\text{ }f\left(-1\right),\text{ }f\left(0\right),\text{ }f\left(1\right),[/latex]and[latex]\text{ }f\left(2\right).[/latex]

1.4 Section Exercises. For each function graphed, estimate the local maximums, local minimums and inflection points. Then specify the intervals on which the function is increasing, decreasing, concave up and concave down.