6. Exponential & Logarithmic Functions

Graph each function. ƒ(x) = (1/10)^-x

Concept Check. If ƒ(x) = a^x and ƒ(3) = 27, determine each function value. ƒ(2)

Graph each function. Give the domain and range. ƒ(x) = (1/3)^-x+1

Solve each equation. 4^x-2 = 2^3x+3

Solve each equation. Round answers to the nearest hundredth as needed. (1/4)^x=64

Graph each function. Give the domain and range. ƒ(x) = (1/3)^x-2 + 2

For ƒ(x) = 3^x and g(x)= (1/4)^x find each of the following. Round answers to the nearest thousandth as needed. ƒ(-1.68)

Graph y= 2^x and x = 2^y in the same rectangular coordinate system.

For ƒ(x) = 3^x and g(x)= (1/4)^x find each of the following. Round answers to the nearest thousandth as needed. ƒ(-5/2)

Graph each function. ƒ(x) = 4^-x

Graph f and g in the same rectangular coordinate system. Then find the point of intersection of the two graphs. f(x) = 2^x, g(x) = 2^-x

The graph of an exponential function is given. Select the function for each graph from the following options:

$f(x) = 3^x, \(\quad\) g(x) = 3^{x-1}, \(\quad\) h(x) = 3^x - 1, \\(\f\)(x) = -3^x, \(\quad\) G(x) = 3^{-x}, \(\quad\) H(x) = -3^{-x}.$

Determine if the function is an exponential function.  

If so, identify the power & base, then evaluate for $x=4$ .

$f\(\left\)(x\(\right\))=3\(\left\)(1.5\(\right\))^{x}$

The graph of an exponential function is given. Select the function for each graph from the following options: f(x) = 4^x, g(x) = 4^-x, h(x) = -4^-x, r(x) = -4^-x+3

In Exercises 5–9, graph f and g in the same rectangular coordinate system. Use transformations of the graph of f to obtain the graph of g. Graph and give equations of all asymptotes. Use the graphs to determine each function's domain and range. f(x) = e^x and g(x) = 2e^x/2