Key Features of Exponential Functions

Which of the following statements are true about the function below? Select all that apply.

 $f\left(x\right)=0.5\left(2\right)^x-1$  

• The function represents exponential growth

• The y-intercept is  $\left(0,\ 0.5\right)$  

• The horizontal asymptote is  $y=-1$  

• The domain is all real numbers  $\left(-\infty,\ \infty\right)$  

• The range is all real numbers  $\left(-\infty,\ \infty\right)$  

Tags

CCSS.HSF.IF.A.1

CCSS.HSF.IF.B.4

CCSS.HSF.IF.B.5

CCSS.HSF.IF.C.7

CCSS.HSF.LE.A.1

Given the function

 $g\left(x\right)=4^{x-2}+3$ , what is the horizontal asymptote? 

•  $y=-2$  

•  $y=2$  

•  $y=-3$  

•  $y=3$  

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

State the range of the function below:

 $h\left(x\right)=-5^x-1$  

• All real numbers  $\left(-\infty,\ \infty\right)$  

•  $y>1$  

•  $y>-1$  

•  $y<-1$  

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

Which equation models the graph?

• $y=1+2x$

• $y=2x$

• $y=1\cdot2^x$

• $y=2\cdot1^x$

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

Which function models exponential decay?

• $f\left(x\right)=5\left(0.99\right)^x$

• $g\left(x\right)=\left(\frac{3}{2}\right)^x+2$

• $h\left(x\right)=1.01^x$

• $y=0.5\left(2\right)^x$

Tags

CCSS.HSF.LE.A.1

CCSS.HSF.LE.B.5

Which of the following statements are true of the exponential function? Select all that apply.

• The graph has been shifted up 3 units from the parent function.

• The y-intercept is $\left(0,\ 1\right)$

• The function represents exponential growth.

• The domain is $x>-2$

• The range is $y>3$

Tags

CCSS.HSF.BF.B.3

CCSS.HSF.IF.B.4

CCSS.HSF.IF.B.5

CCSS.HSF.IF.C.7

CCSS.HSF.LE.A.1

Which function models the values in the table?

• $f\left(x\right)=125\left(5\right)^x$

• $f\left(x\right)=125\left(\frac{1}{5}\right)^x$

• $f\left(x\right)=125-5^x$

• $f\left(x\right)=125-5x$

Tags

CCSS.HSF.BF.A.1

CCSS.HSF.IF.B.4

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

Tags

CCSS.HSF.BF.B.3

Tags

CCSS.HSF.BF.B.3

The population of deer in a certain town was 10,000 in 2015. Each year the population has decreased by 10%. That is, each year the population is 90% of what it was the previous year. Which equation models the population of deer since 2015?

• $d\left(t\right)=10000-90t$

• $d\left(t\right)=10000-10t$

• $d\left(t\right)=10000\left(0.9\right)^t$

• $d\left(t\right)=10000\left(0.10\right)^t$

Tags

CCSS.HSF.BF.A.1

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

CCSS.HSF.LE.B.5