Functions and Translations pt. 1

Updated: 4/28/2020

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Talks about linear, quadratic, and exponential functions and begins to talk about translations.

- Hey did you get the math HW for last night? It was so hard!!
- Yeah, It was actually quite easy I could help you out!
- There are 3 types of equations: Linear, Quadratic, and Exponential
- Linear is an equation between two variables that gives a straight line when plotted on a graph.Form: mx+bExample: y = 2x + 1
- Quadratic function is a function that can be described by an equation of the form fx = ax2 + bx + c, where a ≠ 0. In a quadratic function, the greatest power of the variable is 2.Example: 6x2+5x+6
- The exponential function f with base a isdefined byf(x) = axwhere a > 0, a ≠ 1, and x is any real number.Example: f(x) = 2x
- Are you getting the hang of it?
- Yeah! It's actually quite simple!
- Vertical Shifts- Causes functions to shift up or down Horizontal Shifts- Causes functions to shift to the left or rightReflections- Causes functions to reflect or mirror over the x or y axis
- These functions can go through transformations. There are three,
- When a number is added or subtracted from a function it is a vertical shift. A positive number makes it go up while a negative makes it go down. It is usually in the form: g(x) =bx+c C>0 move upward, C<0 move downward
- Let's start with vertical shifts.
- Oh a vertical shift is like a zipper. When you go up, it's like adding a positive number. When you move it down it's like a negative number.