Suppose f(x) = 3x + 5. Describe how the graph of each function compares to f.

Question

Suppose f(x) = 3x + 5. Describe how the graph of each function compares to f.

1. g(x) = f(x) + 12

2. h(x) = f(x) −7

3. g(x) = f(x + 8)

4. h(x) = f(x − 14)

5. g(x) = 4f(x)

6. g(x) = f(5x)

Answer 1

The two approaches are to just use intuition or know the formulas for transformation.

1. For the first one, we know that it's being translated up 12. Otherwise, we can know the formula f(x) + d, where d represents the shift of f up or down d units.
2. Same thing as 1.
3. Using the formula f(x-c) where c represents a shift left or right, we know f shifts left 8 units
4. Same as 3.
5. ±af(x), where a represents a compression or stretch of the y values. In other words, we take f (which represents y values) and multiply by a. In this case, we multiply y values by 4
6. f(ax), where a represents a compression or stretch of the x values. When a is between 0 and 1, the graph is being stretched (becomes wider), and when a is greater than 1, the graph is compressed (becomes more narrow).

Answer 2