Characteristics of Exponential Functions

Characteristics of Exponential Functions

Exponential Function

Where

• a = Initial value (y-intercept)

• b = Growth factor (if b>1, growth) or Decay factor (if 0<b<1, decay)

Other Key Features

• Y-Intercept: The initial value at x=0.

• Asymptote: The horizontal line the graph approaches but never touches.

• End Behavior: The direction the graph moves as x approaches positive or negative infinity.

• Domain: All possible x-values (usually all real numbers).

• Range: All possible y-values.

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Multiple Choice

What is the initial value of the function? $$f\left(x\right)=3\left(2\right)^x$$

• 2

• 3

• 6

• 5

Multiple Choice

In the function $$f\left(x\right)=6\cdot\left(1.2\right)^x$$ , what does 1.2 represent?

• Growth Factor

• Decay Factor

• Y-Intercept

• Initial Value

Multiple Choice

Which of the following represents exponential decay?

• $$f(x)=5\cdot3^x$$

• $$f(x)=4\cdot2^x$$

• $$f(x)=2\cdot0.5^x$$

• $$f(x)=7\cdot1^x$$

Multiple Choice

What is the domain of any exponential function $$f(x)=a⋅b^x$$ ?

• Positive integers only

• x≤0

• x≥0

• All real numbers

Hotspot

Where is the y-intercept of the graph?

Labelling

Label the y-intercept and rate factor of $$f(x)=2\cdot3^x$$

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Rate Factor

Y-Intecept

Open Ended

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