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| 15 Theory slides |
| 8 Exercises - Grade E - A |
| Each lesson is meant to take 1-2 classroom sessions |
Here are a few recommended readings before getting started with this lesson.
The graph of the exponential function y=(31)x is drawn on the coordinate plane.
Tiffaniqua is beginning to explore the graphs of exponential functions.
She is interested in the graph of the exponential function y=0.5x.
By reflecting this exponential parent function on the corresponding axis, she wants to draw the graphs of the following functions.
In the coordinate plane, the graph of the exponential function y=a(2cx) can be seen. By changing the values of a and c, observe how the graph is vertically and horizontally stretched and shrunk.
Tiffaniqua, feeling good, continues her study of exponential functions.
She considers the exponential parent function y=(31)x and wants to write the function rules of two functions.
The graph of the exponential parent function y=2x is shown in the coordinate plane. The graph of a horizontal or vertical stretch or shrink is also shown.
On her quest to figure out exponential functions, Tiffaniqua has met her match.
She is thinking about the exponential parent function y=4x and wants to write the function rules of two functions.
In the coordinate plane, the graph of the function y=2x−h+k can be seen. By changing the values of h and k, observe how the graph is horizontally and vertically translated.
Tiffaniqua is feeling good about her understanding of the graphs of exponential functions. She is now moving on to mastering another aspect of them.
With translations on her mind, Tiffaniqua has drawn the graph of the exponential function y=3x.
By translating this exponential parent function, she wants to draw the graphs and write the equations of the following functions.
Graph:
Graph:
Graph:
The graph of the exponential parent function y=2x and a vertical or horizontal translation are shown in the coordinate plane.
With the topics learned in this lesson, the challenge presented at the beginning can be solved. The graph of the exponential function y=(31)x is given.
The graph of y=21(31)x+1−2 is a translation 1 unit to the left, followed by a vertical shrink by a factor of 21, and a translation 2 units down of the graph of y=(31)x.
Marcos is in the lab of his biology class. The students are given a microscope to take a look at a population of bacteria.
Marcos wants to conduct a new experiment using twice the initial amount of bacteria. In the given exponential function, the initial population is 10. Therefore, to double the initial amount, we will multiply 10 by 2. r(x)=( 2* 10)* 2^x ⇕ r(x)=20* 2^x By using the Associative Property of Multiplication, the resulting function can be written as 2 times p(x).
This means that the graph of r(x) is a vertical stretch of the graph of p(x) by a factor of 2.
Mark has tried to translate an exponential function 2 units to the right and 1 unit up. He followed the steps shown below. However, his teacher told him that the answer is incorrect.
Mark wants to write an exponential function for the indicated translation of the graph of f(x)=2* 5^x. 1 unit up and 2 units to the right In order to find Mark's mistake, we will begin by recalling two things.
Therefore, for the indicated translation we have to add1 to the output of f(x), and subtract2 from its input. f(x - 2) + 1 = 2* 5^(x - 2) + 1 We notice that Mark added 2 to the input instead of subtracting. This is the mistake. Conversely, the second step is correctly done. Therefore, only step 1 is wrong.