Exponential Functions and Their Graphs

What does the a represent in the equation

 $f\left(x\right)=a\left(b\right)^x$  

• Slope

• Y-intercept

• Rate of Change

• Common ratio

Identify which functions are exponential.

• f(x) = 2x - 5

• g(x) = 3^x

• k(x) = 3x⁴ - 6x + 9

• 
  

  $k\left(x\right)=3\cdot\left(\frac{1}{2}\right)^x$

Tags

CCSS.HSF.LE.A.1

Determine which function models exponential growth.

• $g\left(x\right)=3\cdot2^x$

• $k\left(x\right)=\left(\frac{1}{3}\right)^x$

• $m\left(x\right)=3\cdot\left(\frac{2}{3}\right)^x$

• $p\left(x\right)=4x^2+5x-9$

Determine which functions model exponential decay.

• $g\left(x\right)=3\cdot2^x$

• $k\left(x\right)=\left(\frac{1}{3}\right)^x$

• $m\left(x\right)=3\cdot\left(\frac{2}{3}\right)^x$

• $p\left(x\right)=4x^2+5x-9$

Tags

CCSS.HSF-LE.A.1A

Which equation corresponds to the graph below.

• $k\left(x\right)=3\cdot\left(\frac{1}{2}\right)^x+4$

• $f\left(x\right)=3\cdot2^x+4$

• $f\left(x\right)=3\cdot2^x-4$

• $m\left(x\right)=3\left(\frac{1}{2}\right)^2-4$

Does the equation below represent exponential growth or decay?

 $g\left(x\right)=5\left(\frac{4}{3}\right)^{x-2}-5$  

Given the equation below determine the y-intercept.

 $y=3^x$  

• (0, 1)

• (0, 3)

• x= 0

• y = 0

Tags

CCSS.HSF-IF.C.7E

Given the equation below determine the asymptote.

 $y=3^x$  

• (0, 1)

• (0, 3)

• x= 0

• y = 0

Determine the asymptote of the equation below:

 $g\left(x\right)=4\cdot2^x+3$  

• y = 4

• y = 2

• y = 3

Evaluate the following. Round to the nearest thousandths.

 $e^{2.3}$