# Graphing Sample Problems

Please help with the following problems.

1. Express each function graphed in terms of a base function.

2. Sketch the graph of a function based on a given base function.

For example: Given f(x), sketch: f(x+3).

See the attached file.

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## SOLUTION This solution is **FREE** courtesy of BrainMass!

See the attached file.

I could not see #5 - 12 clearly, but I can still instruct you on how to complete the assignment.

What to do:

1. Each graph should be like f(x) but with a change. (Please see attached PDF file for a description and examples of each type of transformation.)

You need to look at each graph and ask yourself, relative to f(x) what happened?

Example a: if the graph moved to the right, then that's a horizontal shift expressed as f(x+c).

So if it moved 5 to the right, your answer would be f(x-5).

Question: How do you know how many it moved? Still with f(x-5).

Answer: Pick any point on f(x). Get the x-value, call it x1. Stay at that same height (i.e. same y-value) and move your hand horizontally only (i.e. to the right) until you touch the second graph. Read the x-value for the point on the second graph, x2. c = x2 - x1.

Note: For parabolas, the vertex is an excellent point to use as a reference.

Example b:

So if your graph looks like f(x) but upside down, then that's a reflection and the answer would be - f(x) i.e. negative sign then f(x).

Remember to look at each graph only relative to the original f(x).

#13 - 20

2. Here they have given you the original f(x) and are asking you to draw what happens.

For example: 13. f(x+3) means a horizontal shift to the LEFT 3.

So draw the exact same shape as f(x) but moved to the LEFT 3.

For accuracy, pick maybe five points on f(x) and move each point to the LEFT 3 then connect the dots.

Like (2, 0) would move to (2 - 3, 0) = (-1, 0) subtract 3 from the x-coordinate to move left

(1, 1) would move to (1-3, 1) = (-2, 1) and so on.

If you need to do two transformations, complete them one at a time. Using the new graph as the "original" for the next shift.

For example: 2*f(x - 4) This graph will have y-values that are twice as large as f(x) and move to the RIGHT 4

First, move to the RIGHT 4, using the procedure above. (2, 0) becomes (2, 0+4) = (2, 4) etc to get f(x-4)

Second, multiply each y-value of f(x-4) by 2 to get 2*f(x-4)

e.g. (2, 4) becomes (2, 4*2) = (2, 8).

Make sure you are multiplying the y-value of the shifted function.

#21

3. Here you are only being asked to describe the transformation

e.g. f(x + 3) means "Horizontal Shift to the left 3."

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