Graphing functions

Each group will be given a type of function to graph and explore how constants affect each type of graph.

1a. Let d∈{-2, -1, 0, 1, 2}. Graph f(x)+d for each value of d.

1b. Describe how f(x)+d affects the graph as a whole.

2a. Let c∈{-2, -1, 0, 1, 2}. Graph f(x+c) for each value of c.

2b. Describe how f(x+c) affects graph as a whole.

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3a. Let a∈{1/4, 1/2, 1, 2, 4}. Graph a*f(x) for each value of a.

3b. Describe how a*f(x) affects:

y-intercept -

x-intercept(s) -

the graph as a whole -

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3c. Describe how -a*f(x) affects a*f(x).

4a. Let b∈{1/4, 1/2, 1, 2, 4}. Graph f(b*x) for each value of b.

4b. Describe how f(b*x) affects:

y-intercept -

x-intercept(s) -

the graph as a whole -

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4c. Describe how f(-b*x) affects f(b*x).

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5. Summarize the effects of a*f(b*x + c) + d by filling in the blanks below using the following choices:

• positive, or negative,
• horizontal, or vertical,
• shift, compression, or stretch.

1. If d>0, then f(x)+d is a ____________ ____________ ____________ of f(x).
2. If d<0, then f(x)+d is a ____________ ____________ ____________ of f(x).
3. If c>0, then f(x+c) is a ____________ ____________ ____________ of f(x).
4. If c<0, then f(x+c) is a ____________ ____________ ____________ of f(x).
5. If a>1, then a*f(x) is a ____________ ____________ of f(x).
6. If 0<a<1, then a*f(x)is a ____________ ____________ of f(x).
7. If b>1, then f(b*x) is a ____________ ____________ of f(x).
8. If 0<b<1, then f(b*x) is a ____________ ____________ of f(x).

6. Which constants affect the graph horizontally? vertically?

7. Which constants affect the graph's inputs? outputs?

Vocabulary