PC Chapter 3 Mid Review: Exponential & Logarithmic Functions

Describe the domain, range, and where the function is increasing or decreasing.

$$f\left(x\right)=5^{-x}$$

Domain:​ (a)  

Range:​ (b)  

The function is ​ (c)  

Describe the intercepts, asymptotes, and end behavior of the function.

$$f\left(x\right)=5^{-x}$$

y-intercept: ​ (a)  

asymptote: x = ​ (b)  

$$\lim_{x\rightarrow-∞}\left(x\right)\ =$$ ​ (c)  

$$\lim_{x\rightarrow∞}f\left(x\right)=$$ ​ (d)  

Describe the domain, range and whether the function is increasing or decreasing.

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

Domain:​ ​ (a)  

Range:​ (b)  

The function is ​ (c)  

Describe the intercepts, asymptotes, and end behavior of the function

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

y-intercept: ​ (a)  

asymptote: y=​ (b)  

$$\lim_{x\rightarrow-∞}f\left(x\right)=$$ ​ (c)  

$$\lim_{x\rightarrow∞}f\left(x\right)=$$ ​ (d)  

Match the following graphs to their equation.

Describe the transformation that results in the graph of g(x) from f(x).

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

Describe the transformation that results in the graph of g(x) from f(x).

$$f\left(x\right)=\left(3\right)^{x\ }$$ and $$g\left(x\right)=2\left(3\right)^{x-2}$$

Choose all that apply!

Describe the transformation that results in the graph of g(x) from f(x).

$$f\left(x\right)=e^x$$ and $$g\left(x\right)=-e^x-6$$

Choose all that apply!

Describe the transformation that results in the graph of g(x) from f(x).

$$f\left(x\right)=10^x$$ and $$g\left(x\right)=10^{2x}$$

In the formula for compound interest, $$A=P\left(1+\frac{r}{n}\right)^{nt}$$ , which variable has NO effect on the amount of time it takes an investment to double?