Unit 1.2 Interpreting Graphs and Using Graphical Models

“An exponential equation is one where the variable occurs in the-”

“-exponent”

How would you graph 3^x = 7

• First graph y = 3^x

• Then graph y = 7

• Note the point of intersection, about (1.7, 7)

• This MUST mean that for 3^x = 7 x will be 1.7

In a graph of soda sales and advertisements, is sales increase then taper off, what could this indicate?

A saturation point. Having more ads won’t increase sales

“If a graph increases to the right, it has a ____ rate of change”

Positive

“If a graph decreases to the right, it has a ____ rate of change”

Negative

“A steeper graph means a ____ rate of change”

Greater

“A horizontal line indicates that the rate of change is ____ (there is no change in y for any change in x”

Zero

“If the graph is a straight line, the rate of change is ____”

Constant

“The rate of change is changing/variable if the graph is ____ “

Non-linear

“The rate of change refers to the ____ of the graph”

Steepness

The rate of change is more commonly known as what?

Slope

The rate of change/slope is most easily calculated when?

When there’s a straight line because there is a constant rate of change

“A curved line would have ____ at different points on the graph”

Varying slopes

What is the equation for slope in words?

Slope = rise/run

What does rise and run mean?

• Rise is the vertical distance

• Run in the horizontal distance

What letter represents slope?

m

What is the equation for slope using letters?

Besides m, what other letter can slope be represented by?

a

Can any two points on a graph be selected to calculate slope?

Yes

When calculated the rate of change, what’s something to remember about the names of the x and y axes?

They will be related to each other like km per hour, dollar per hour etc.

If you’re graphing an equation like 10(5)^x = 150 what is something you ALWAYS need to remember to do first?

Remove that first number by dividing both sides by 10