Precalculus & Trignometry

Objectives:  Recognize the graphs of parent functions.  Right now, you are responsible for  Linear functions  Quadratic functions (squaring function)  The square root function  The cubic function  The cube root function  Reciprocal functions  Absolute Value function  Graph all of the above functions  Differentiate between even and odd functions

Even functions  Symmetric with respect to the y-axis

Odd functions

Linear Functions

Graph of the parent linear function

Quadratic Functions

Graph of the parent quadratic function

Square Root Function

The parent square root function X values that are not perfect Squares will lead to Irrational y values which are Very difficult to plot

Cubic Function

Graph of the Cubic Parent Function

Cube Root Function

Graph of the Cube Root Function Using x values that are not Perfect cubes will result in Irrational y values that are Very difficult to plot.

The Reciprocal Function

Graph of the Reciprocal Function Do not allow the graph to touch or Cross the x-axis or the y-axis. Plot (1, 1) and draw a curve Plot (-1, -1) and draw a curve.

Absolute Value Function

Graph of the Absolute Value Function Plot (0, 0) and then graph a Slope of positive 1 to the right And a slope of negative 1 to The left to create a V shape.

Practice Graphing

Transformations of Parent Functions  Shift functions vertically (up and down)  Shift functions horizontally (left and right)  Stretch and compress functions vertically  Reflect functions over the x and y axis

Vertical & Horizontal Shifts just moves the graph does not change shape

Example from Desmos

Another Example from Desmos

Vertical Stretches and Compressions

Reflections

Desmos Example

What you will need to be able to do:  At this point, you should be able to graph al of the parent functions.  You should then be able to look at an equation of a function, know which parent function it represents, and then apply the correct transformations to graph the new function.

 You should be able to ignore the “-3” and “+4” and realize that this is just a parabola; however, the parent function has been shifted to the right 3 and up 4 units.  To graph it, you just shift each original point from the parent function right 3 and up 4.

Graphs of the example II

Graphs

A Gift for Making it Through this Presentation  Here’s a chance for bonus. The first 20 s that I receive with the correct answer will be awarded the bonus points.  You must explain your work in the to receive credit.  You must also provide me with a written copy of your work when we return to school, or you will lose the bonus points.  Go to the next slide for the problem.

A Rose Garden  Suppose that you are working for the mayor of Pittsburgh. Your job is to complete a project that would add a border of yellow roses around an existing rectangular rose garden. The current rose garden is 12 ft long and 5 ft wide and contains only red roses. The yellow rose border should be the same width (thickness) on all 4 sides and should have the same area as the current red rose garden (because the planning committee bought the same number of red and yellow roses to begin with, and we don’t want to waste roses!)  Determine the width of the yellow rose border to the nearest tenth of a foot.

A little help ? I want the width/thickness of the yellow rose border. That is the same on all 4 sides. It’s the distance from the outer edge of the red roses to the outer edge of the yellow Rose border. I marked it with a green line for you.