Section 1.5
Video 1: Function Transformations: A Summary.
Starting with a function f(x) and then including constants a, b, c, and d as shown in the clip above results in the more complicated function on the right.
What is the effect of multiplying the function f by a?
When a > 1?
When 0 < a < 1?
What is the effect of multiplying the variable x by b on the inside of the function?
When b < 1?
When 0 < b < 1?
What is the effect of adding c to x on the inside of the function?
When c > 0?
When c < 0?
What is the effect of adding d to f on the outside of the function?
When d > 0?
When d < 0?
Answer the question in the clip above. Describe all the changes to the parent function?
What was the parent function?
What changes were made to the parent function?
Answer the question in the clip above. Describe all the changes to the parent function?
What was the parent function?
What changes were made to the parent function?
Notice that any changes that occur inside the function have a horizontal effect while any changes outside the function have a vertical effect.
Video 2: Horizontal and Vertical Stretches and Compressions.
Use the information in the video to fill out the 3 charts.
x y x y x y
1 1 1
2 2 2
3 3 3
4 4 4
What effect does the 2 have in the function to the right?
What effect does the ½ have in the function to the left?
In the snip above, what effect does the 3 have?
In the snip above, what effect does the 2 have?
Video 3: Vertical and Horizontal Shifts
Fill out the two tables above to see the effect of subtracting 1 from x inside the function.
Describe what happens when we go from f(x) to f(x+c) and when we go from f(x) to f(x-c).
Fill out the two tables above to see the effect of subtracting 2 from f outside the function.
Describe what happens when we go from f(x) to f(x) + d and when we go from f(x) to f(x) – d.
Describe both shifts in the function above. (Left/right and up/down and by how much for each shift).
Describe both shifts in the function above. (Left/right and up/down and by how much for each shift).
Video 4: Reflections across the x-axis and y-axis.
Thinking back to our transformation of f(x) to af(b(x+c))+d it is the a and the b that are responsible for reflections across the x and y axis.
Describe the reflection when a<0.
Describe the reflection when b<0.
Fill in the missing y values in the 3 charts in the snip above. You are welcome to either write on the snip or to make your own charts.
Graph both f(x) = -|x| and g(x) = |x| on the snip above. This will put them both on the same graph.
Graph both f(x) and g(x) shown above on the graph in the snip. Plot at least 3 points on the original f(x) graph and plot the reflections of these 3 points on the g(x) graph.
Video 5: Multiple Transformations Part 1
The graph above is for f(x) = |x|. Graph the function given in the snip in the space to the right of the snip and show your work below.
The graph above is for f(x) = Graph the function given in the snip in the space to the right of the snip and show your work below.
Video 6: Multiple Transformations Part 2.
The graph above is for f(x) = x2 . Graph the function given in the snip in the space to the right of the snip and show your work below.
The graph above is for f(x) = . Graph the function given in the snip in the space to the right of the snip and show your work below.
Video 7: Even and Odd functions
If a function is even then If a function is odd then
f(x) = -f(x) =
How can you tell whether or not a polynomial is even?
How can you tell whether or not a polynomial is odd?
NOTE: Most polynomials are neither even nor odd because they have a mix of even and odd exponents.
Is f(x) = x2 even, odd, or neither and why? Is f(x) = x3 even, odd, or neither and why?
Further application: Is f(x) = 4×3 – 5×2 even, odd, or neither?
Answer: Neither because the polynomial has both even and odd exponents.
Section 1.6
Video 1: Inverse functions
If a function is not 1 to 1, does it have an inverse function?
What test can we use to determine if a function is 1 to 1. Note that the vertical line test tells us whether or not f(x) is a function.
If f(x) and g(x) are inverses of each other, what does f(g(x)) = and what does g(f(x)) =
The video gives a 3 step process for finding the inverse function of a given function. What are the 3 steps?
1.
2.
3.
Answer the questions in the snip above. Notice that they have told us the functions are 1 to 1 so you can skip step 1 of the process.
Find the inverse functions of the given 1 to 1 functions in the snip above.
Video 2: Determine if a Relation given as a table is a 1 to 1 function
See the 3 relations given as tables in the snip above. Call the first table A, the second table B, and the third table C. Tell whether each table is a function and why. Also tell whether each table is 1 to 1 and why.
Table A
Table B
Table C
Video 3: Restricting the domains of functions that are not 1 to 1.
What is the original domain of the function f(x) in the snip above?
What is the restricted domain shown in the video that makes f be 1 to 1?
Both the original and the restricted version of the function have the same range. What is this range?
Find f-1(x). Show your work.
What are the domain and range of f-1(x)?
The post Section 1.5 Video 1: Function Transformations: A Summary. Starting with a function appeared first on PapersSpot.
