Linear vs Exponential Functions

Linear and Exponential Functions

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Linear Functions

• On a Graph: straight line

• In a Table: ADD or SUBTRACT the same amount to the y-values

• In an Equation: y=mx+b

Exponential Functions

• On a Graph: curved line (not a u)

• In a Table: MULTIPLY or DIVIDE the same number to the y-values

• In an Equation: y=a(b)^x

Multiple Choice

Is the graph linear, exponential or neither?

• Linear
• Exponential
• Neither

Multiple Choice

Is the equation linear, exponential or neither?

• Linear
• Exponential
• Neither

Multiple Choice

Is the equation linear, exponential or neither?

• Linear

• Exponential

• Neither

Multiple Choice

Is the graph linear, exponential, or neither?

• Exponential

• Neither

• Linear

Multiple Choice

Does the table show a function that is linear, exponential, or neither?

• Linear

• Exponential

• Neither

Multiple Choice

Does the table show a function that is linear, exponential, or neither?

• Linear

• Exponential

• Neither

Linear Functions (y=mx+b)

• m: slope (rise/run or change in y/change in x)

• b: y-intercept (where the lines crosses the y-axis or the y-value when x=0)

Multiple Choice

Give the equation for the graph

• y = 5x - 3
• y = 4x + 2
• y =-2x + 5
• y = - 2x + 4

Multiple Choice

What is the equation for the linear table?

• y = 7x + 3

• y = 3(7)^x

• y = 7(3)x ^{- 1}

• Not a function

Exponential Functions (y=a(b)^x)

• a: y-intercept (where the curve crosses the y-axis or the y-value when x=0)

• b: growth or decay factor (what is being multiplied or divided when you look at the y-values)

• Growth if b>1

• Decay if b is between 0 and 1

Multiple Choice

What is the y-intercept of the function?

• 2

• 3

• 1

• -2

Multiple Choice

What exponential equation would be represented by this table?

• y = 3(4)^x

• y = 3x + 4

• y = 4(3)^x

• y = 4x + 3