1. UNDERSTANDING VARIOUS FUNCTIONS RICHARDSON 423 MATH 2

2. UNDERSTANDING VARIOUS FUNCTIONS We have discussed what functions are, what they do singularly, as well as combined with a different function. We practiced operations of functions (addition, subtraction, multiplication, and division) Now we discuss the various forms of functions that we see in mathematical form and by graphical form.

3. TYPES OF FUNCTIONS Functions come in various form because they are deviations from the parent functions. What is a parent function? A parent function is the simplest function of a family of functions that preserves the definition (or shape) of the entire family. What does a parent function look like? Parent functions look different dependent on the type of function we are deviating from. Look at the following types and see what we mean?

4. 1.LINEAR FUNCTION The Parent Function for a linear function is f(x)=x or commonly known as y=x. From this expression we begin seeing variations in functions from this parent function.

5. 2. CONSTANT FUNCTION a constant function is a function whose (output) value is the same for every input value. This function is seen as f(x)=a, {a is a real number)

6. 3. QUADRATIC FUNCTION A quadratic function is one of the form f(x) = ax 2 + bx + c, where a, b, and c are numbers with a not equal to zero. The graph of a quadratic function is a curve called a parabola. Parabolas may open upward or downward and vary in "width" or "steepness", but they all have the same basic "U" shape.

7. 4. ABSOLUTE VALUE FUNCTION An absolute value function is a function that contains an algebraic expression within absolute value symbols. Recall that the absolute value of a number is its distance from 0 on the number line. Absolute functions are written as f(x)=IXI WEBSITE ABOUT ABSOLUTE VALUE FUNCTIONS WEBSITE ABOUT ABSOLUTE VALUE FUNCTIONS

8. Understanding Linear Equations So we discussed the difference between equations and functions. Equations can have multiple output values while functions detail single input/single output values. So what does exactly is the difference between Linear Equations and Linear Function? A linear equation that makes a straight line when it is graphed but it is not necessarily restrained to follow the requirements of the vertical line test. Let’s look at the following diagrams to understand linear equations more.

9. LINEAR EQUATION An equation that makes a straight line when it is graphed. Often written in the form: y=mx+b Y=how far up does the equation start X=how far across the equation go M=slope B= the y-intercept(where the line crosses the y-axis)

10. Okay! SO LET’S DO SOME PRACTICE PROBLEMS PLEASE PAY ATTENTION TO MR. HERB, TO BEGIN PRACTICE ON THE POWERPOINT