<meta http-equiv="refresh" content="1; url=/nojavascript/"> Combining Transformations ( Study Aids ) | Analysis | CK-12 Foundation
You are viewing an older version of this Study Guide. Go to the latest version.

# Combining Transformations

%
Best Score
Best Score
%
Transforming Functions
0  0  0

### Vocabulary

 Word Definition ____________ Also called translation or slide; a transformation applied to the graph of a function which does not change the shape of the graph, only the location ____________ a result of adding a constant term to the value of a function; moves up or down Horizontal Shift _________________________________________________________________ Reflection _________________________________________________________________ ____________ A transformation which results in the width of a graph being increased or decreased; the result of the co-efficient of the x term being between 0 and 1. Compression _________________________________________________________________

What transformations must be applied to $y = x^{2}$ , in order to graph $g(x) = 3(x - 4)^{2} + 2$ ?

### Practice

1. If a function is multiplied by a coefficient, what will happen to the graph of the function?
2. What does multiplying x by a number greater than one create?
3. What happens when we multiply x by a number between 0 and 1
4. In order to obtain a reflection over the y axis what do we have to do to x?
5. How do we obtain a reflection over the x-axis?
6. Write a function that will create a horizontal compression of the following: $f(x) = x^2 + 3$
7. Write a function that will horizontally stretch the following: $f(x) = x^2 - 6$
8. Rewrite this function $f(x) = -\sqrt{x}$ to get a reflection over the x-axis.
9. Rewrite this function $f(x) = \sqrt{x}$ to get a reflection over the y-axis.
##### Graph each of the following using transformations. Identify which transformations are used.
1. $f(x) = |x-3| + 4$
2. $h(x) = \sqrt{x + 7}$
3. $g(x) = \frac{1}{x - 5}$
4. $f(x) = -3x^3$
5. $h(x) = (x - 7)^3 + 4$
6. $f(x) = \frac{1}{4}(x - 9)^2 + 5$
7. $f(x) = 3\sqrt{x + 2} - 6$
8. $f(x) = \frac{3}{4(x + 5)} + \frac{4}{5}$
1. What part of the function $g(x) = -(f(x) + 1) = -(x^3 + 1)$ shifts the graph of $f(x)$vertically?
2. What part of the function $g(x) = -(f(x) + 1)$ reflects the graph of $f(x)$ across the x-axis?
3. What is different between the functions $g(x) = -(x^3 + 1.0)$ and $h(x) = -x^3 + 1.0$ that changes the appearance of the graph?
4. Write a function $g(x)$ whose graph looks like the graph of $f(x) = |x|$ reflected across the x-axis and shifted up 1 unit. $g(x) =$
5. How do you transform the graph of: $f(x) = x^3$ so that it looks like the graph of:$f(x) = 4x^3 + 6$
1. Stretch it by a factor of ¼ and shift it up 6 units.
2. Stretch it by a factor of 6 and shift it left 4 units.
3. Stretch it by a factor of 4 and shift it down 6 units.
4. Stretch it by a factor of 4 and shift it up 6 units.

Click for more help on: