Graph Analysis of Logistic Functions (MA 4.21/22.2022)

Which of the following functions is logistic?

• $f\left(x\right)=-2\log_ex$

• $f\left(x\right)=\ln\left(x+2\right)$

• $f\left(x\right)=\frac{1}{1+e^{-0.1x}}$

• $f\left(x\right)=4e^{\left(x-1\right)}$

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

Which of the following logistic functions has an a-value equal to 4?

• $g\left(x\right)=\frac{32}{1+3e^{-4x}}$

• $g\left(x\right)=\frac{4}{1+2e^{-0.5x}}$

• $g\left(x\right)\ =\frac{79}{1+4e^{-0.125x}}$

• $g\left(x\right)=\frac{8}{1+8e^{4x}}$

Tags

CCSS.HSF.LE.A.2

Find the upper asymptote for the logistic function  $f\left(x\right)=\frac{60}{1+4e^{-2x}}$ .

•  $y=60$  

•  $y=120$  

•  $y=15$  

•  $y=12$  

Tags

CCSS.HSF-IF.C.7E

Which of the following logistic functions has an asymptote at y = 8?

• $y=\frac{8}{1+2e^{-0.5x}}$

• $y=2e^{-0.5x}+8$

• $y=\ln\left(x-8\right)$

• $y=\frac{8}{1-e^x}$

Tags

CCSS.HSF-IF.C.7E

What is the value of a in the logistic function  $y=\frac{6}{1+3e^{-2x}}$  ?

•  $a=1$  

•  $a=2$  

•  $a=3$  

•  $a=6$  

Tags

CCSS.HSF.LE.A.2

What is the value of c in the logistic function  $y=\frac{75}{1+24e^{-0.125x}}$  ?

•  $c=24$  

•  $c=0.125$  

•  $c=25$  

•  $c=75$  

Find the value of c in the equation of the graphed logistic function:

• $c=2$

• $c=4$

• $c=3$

• $c=1$

Tags

CCSS.HSA.REI.D.11

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

CCSS.HSF.LE.A.1

Find the y-intercept of  $f\left(x\right)=\frac{8}{1+5e^{-\frac{1}{2}x}}$  

•  $\left(0,\ 1.\overline{3}\right)$  

•  $\left(0,\ 2\right)$  

•  $\left(0,\ 13\right)$  

•  $\left(0,\ 4\right)$  

Tags

CCSS.HSF-IF.C.7E

Which of the following gives the correct y-intercept for any logistic function  $f\left(x\right)=\frac{c}{1+ae^{-bx}}$  ?

•  $\left(0,\ \frac{c}{1+ae}\right)$  

•  $\left(0,\ \frac{c}{1-a}\right)$  

•  $\left(0,\ c\right)$  

•  $\left(0,\ \frac{c}{1+a}\right)$  

Tags

CCSS.HSF-IF.C.7E

Find the point where the rate of growth is at its highest in the function $y=\frac{16}{1+4e^{-0.24x}}$  .

•  $\left(5.8,\ 8\right)$  

•  $\left(16.6,\ 8\right)$  

•  $\left(0,\ 8\right)$  

•  $\left(4.2,\ 8\right)$