I REALLY NEED HELP HERE, I AM HORRIBLE AT MATH!
Answer the following questions using what you've learned from this unit. Write your answers in the space provided. Be sure to show all work.
1. Show that the function is the inverse of f(x) = 5x + 2.
Step 1: The function notation f(x) can be written as a variable in an equation. Is that variable x or y?
____
Write f(x) = 5x + 2 as an equation with the variable you chose above. (2 points)
Step 2: Switch the variables in the equation from Step 1. Then solve for y. Show your work. (2 points)
Step 3: Find the inverse of . What does this tell you about the relationship between f(x) = 5x + 2 and g(x)? Show your work. (3 points)
2. The table shows values that represent a function.
x
–2
–3
6
7
5
y
4
2
1
3
4
Part I: Write values that represent the inverse of the function represented in the table above. (3 points)
x
y
Part II: Is the inverse a function? Explain your answer. (2 points)
Remember that in a function, each input value can have only one output value.
3. The graph of f(x) = |x| is shown below. Write the equation for the stretched graph, g(x).
Step 1: Start with the equation g(x) = k • f(x). Substitute the known point and solve for k. Show your work. (2 points)
Step 2: Use the value of k that you found in Step 1 to write an equation for g(x). (1 point)
4. Use the functions below to complete Parts I and II.
f(x) = x2 g(x) = (x – 3)2 + 2
Part I: The graph of f(x) is shown below. g(x) has the same shape as f(x), but is shifted as described by the equation g(x) = (x – 3)2 + 2. Draw and label the graph of g(x) on the same grid as f(x). (3 points)
HINT: Making a table of values for g(x) may help you to graph it.
Part II: Describe how the graph of g(x) relates to the graph of its parent function, f(x). (3 points)
HINT: Think about how f(x) was shifted to get g(x).
5. Use the functions below to complete Parts I and II.
f(x) = |x| g(x) = |x + 2| – 3
Part I: Graph f(x) and g(x) on the grid below. Label each graph. (6 points)
HINT: Making a table of values for each function may help you to graph them.
Part II: Describe how the graph of g(x) relates to the graph of its parent function, f(x). (3 points)
HINT: Think about how f(x) was shifted to get g(x).
6. Use the facts and graph below to write the equation for g(x).
FACTS
This graph shows g(x).
It looks like the graph of the parent function f(x) = x2. However:
It has been reflected (flipped) over the x-axis.
It has been shifted down 4 units.
It has been shifted left 1 unit.
Step 1: Start with the equation f(x) = x2. Write the equation for the graph of g(x) that has been reflected, or flipped, over the x-axis. (2 points)
Step 2: Use the equation you wrote in Step 1. Write the equation for the graph of g(x) that has also been shifted down 4 units. (2 points)
Step 3: Use the equation you wrote in Step 2. Write the equation for the graph of g(x) that has also been shifted left 1 unit. (2 points)
7. Use the facts and graph below to write the equation for g(x).
FACTS
This graph shows g(x).
It looks like the graph of the parent function f(x) = |x|. However:
It has been vertically stretched by a factor of 2.
It has been reflected (flipped) over the x-axis.
It has been shifted down 3 units.
It has been shifted right 1 unit.
Step 1: Start with the equation f(x) = |x|. Write the equation for the graph of g(x) that has been stretched vertically by a factor of 2. (2 points)
Step 2: Use the equation you wrote in Step 1. Write the equation for the graph of g(x) that has also been reflected, or flipped, over the x-axis. (2 points)
Step 3: Use the equation you wrote in Step 2. Write the equation for the graph of g(x) that has also been shifted down 3 units. (2 points)
Step 4: Use the equation you wrote in Step 3. Write the equation for the graph of g(x) that has also been shifted right 1 unit. (2 points)
8. Graph each function on the given coordinate plane.
A.
Graph this step function on the coordinate grid. (3 points)
B.
Graph this piecewise function on the coordinate grid. One piece is graphed for you. (3 points)
