f(x) = b x for b > 0 and b 1

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Cecil Thomas
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1 7. Introduction to Eponential Functions Name: Recall - Eponents are instructions for repeated multiplication. a. 4 = ()()()() = b. 4 = c.!!!! = Properties of Eponential Functions Parent: Why is the parameter called b? f() = b for b > and b In equations like y = m + b, where and y represent the input and output, m and b are referred to as parameters. Parameters are replaced with specific values. Investigating graphs of eponential functions. a. Complete the table and graph f() =. y Use your calculator to check your graph and table. The graph appears to stop at = 3. Check your table. Does the graph really stop here? Use the table in your calculator to correctly etend your graph to the left and right. An asymptote is an invisible line that the graph approaches but never crosses. Asymptotes are written as equations of lines. The graph of the function f() = has a horizontal asymptote at. Find the domain and range.

2 b. On the same ais, graph f() = 3 and label it f(). Graph g() = 5 and label it g(). What parts of the graphs are the same? Are the graphs increasing or decreasing? How does changing the value of b change the graph? Eponential Growth occurs when b >. Larger values of b increase at a faster rate. Eponential Decay occurs when < b <. Smaller values of b decrease at a faster rate. c. Complete the table and graph f() =.! y What is the y- intercept? What is the equation of the asymptote? Is the graph increasing or decreasing? Find the domain and range. d. On the ais above, graph g() = 3 3 Graph h() = and label it h(). 4 and label it g(). What parts of the graph are the same? How does changing the value of b change the graph?

3 Constraints on the value of b Eponential functions are defined only for values of b > and b. b > means two things. Why can t there be negative values for b? Create a table and graph y =!. ( ) y What would the graph look like if b =? What would the graph look like if b =? Standard Form of an Eponential Function Standard Form: f() = ab + q for b > and b Use your calculator to create a table and graph f() = 3! a. What is the y- intercept? What value in the equation changed the y- int.? b. Does this equation model What value in the equation indicates this? c. What is the equation of the asymptote? What value in the equation indicates this?

4 Practice:. On the coordinate plane, graph and label each of the following eponential function. a. f() = b. g() = 3 c. h() = (3) +. Complete the table for each function. f() g() h() - intercept(s): - intercept(s): - intercept(s):

5 3. Graph the functions f() =, g() = and h() = on the same grid for 5. Label your graphs. f() g() h() a. What type of function is each? f() : g() : h() : b. All of these functions have a rate of change for any specified interval. Which function shows an average or constant rate of change? What is that rate of change? c. For the interval 4, find the rate of change for each function. f() : g() : h() : Which function shows the fastest rate of change for this interval? d. Evaluate each functions for =. f() = g() = h() = Which function shows the fastest rate of growth in its y values overall?

We want to determine what the graph of an exponential function y = a x looks like for all values of a such that 0 < a < 1

Section 5 2B: Graphs of Decreasing Eponential Functions We want to determine what the graph of an eponential function y = a looks like for all values of a such that 0 < a < We will select a value of a