# Introduction to Exponential Functions - Video Tutorials & Practice Problems

## Exponential Functions

Determine if the function is an exponential function.

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

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

Exponential function, $f\left(4\right)=16$

Exponential function, $f\left(4\right)=-16$

Not an exponential function

Determine if the function is an exponential function.

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

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

Exponential function, $f\left(4\right)=410.06$

Exponential function, $f\left(4\right)=15.19$

Not an exponential function

Determine if the function is an exponential function.

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

$f\left(x\right)=\left(\frac12\right)^{x}$

Exponential function, $f\left(4\right)=\frac{1}{16}$

Exponential function, $f\left(4\right)=-16$

Not an exponential function

## Do you want more practice?

- In Exercises 1–10, approximate each number using a calculator. Round your answer to three decimal places. 2^3....
- Fill in the blank(s) to correctly complete each sentence. If ƒ(x) = 4^x, then ƒ(2) = and ƒ(-2) = ________.
- In Exercises 1–4, the graph of an exponential function is given. Select the function for each graph from the f...
- In Exercises 1–10, approximate each number using a calculator. Round your answer to three decimal places. 4^-1...
- In Exercises 1–10, approximate each number using a calculator. Round your answer to three decimal places. e^2....
- In Exercises 5–9, graph f and g in the same rectangular coordinate system. Use transformations of the graph of...
- Solve each equation. Round answers to the nearest hundredth as needed. x^(2/3) =36
- Use the compound interest formulas to solve Exercises 10–11. Suppose that you have $5000 to invest. Which inve...
- In Exercises 11–18, graph each function by making a table of coordinates. If applicable, use a graphing utilit...
- In Exercises 11–18, graph each function by making a table of coordinates. If applicable, use a graphing utilit...
- For ƒ(x) = 3^x and g(x)= (1/4)^x find each of the following. Round answers to the nearest thousandth as needed...
- In Exercises 11–18, graph each function by making a table of coordinates. If applicable, use a graphing utilit...
- In Exercises 19–24, the graph of an exponential function is given. Select the function for each graph from the...
- For ƒ(x) = 3^x and g(x)= (1/4)^x find each of the following. Round answers to the nearest thousandth as needed...
- In Exercises 19–24, the graph of an exponential function is given. Select the function for each graph from the...
- In Exercises 25-34, begin by graphing f(x) = 2^x. Then use transformations of this graph to graph the given fu...
- For ƒ(x) = 3^x and g(x)= (1/4)^x find each of the following. Round answers to the nearest thousandth as needed...
- In Exercises 25-34, begin by graphing f(x) = 2^x. Then use transformations of this graph to graph the given fu...
- Graph each function. See Example 2. ƒ(x) = (1/3)^x
- In Exercises 25-34, begin by graphing f(x) = 2^x. Then use transformations of this graph to graph the given fu...
- Graph each function. See Example 2. ƒ(x) = 4^-x
- The figure shows the graph of f(x) = e^x. In Exercises 35-46, use transformations of this graph to graph each ...
- The figure shows the graph of f(x) = e^x. In Exercises 35-46, use transformations of this graph to graph each ...
- The figure shows the graph of f(x) = e^x. In Exercises 35-46, use transformations of this graph to graph each ...
- In Exercises 47–52, graph functions f and g in the same rectangular coordinate system. Graph and give equation...
- Graph each function. Give the domain and range. See Example 3. ƒ(x) = 2^(x+2) - 4
- In Exercises 47–52, graph functions f and g in the same rectangular coordinate system. Graph and give equation...
- Use the compound interest formulas A = P (1+ r/n)^nt and A =Pe^rt to solve exercises 53-56. Round answers to t...
- Use the compound interest formulas A = P (1+ r/n)^nt and A =Pe^rt to solve exercises 53-56. Round answers to t...
- Use the compound interest formulas A = P (1+ r/n)^nt and A =Pe^rt to solve exercises 53-56. Round answers to t...
- Graph each function. Give the domain and range. See Example 3. ƒ(x) = (1/3)^(-x+1)
- Graph y= 2^x and x = 2^y in the same rectangular coordinate system.
- Graph each function. Give the domain and range. See Example 3. ƒ(x) = -(1/3)^(x+2) - 1
- Solve each equation. See Examples 4–6. 4^(x-2) = 2^(3x+3)
- Graph f(x) = 2^x and its inverse function in the same rectangular coordinate system.
- Solve each equation. See Examples 4–6. (√2)^(x+4) = 4^x
- Concept Check. If ƒ(x) = a^x and ƒ(3) = 27, determine each function value. ƒ(-1)