b Use the fact that the graph is symmetric about a certain value of x.
C
c Can the function be negative for any value of x?
D
d Use that the graph is symmetric about a certain value of x.
E
e Try to use the fact that each of the graphs is symmetric about a certain x-value.
A
aInput Value of the Smallest Output: x=2
Input Value of the Largest Output: Does not exist.
B
bInput Value of the Smallest Output: x=0
Input Value of the Largest Output: Does not exist.
C
cInput Value of the Smallest Output: x=- 3
Input Value of the Largest Output: Does not exist.
D
dInput Value of the Smallest Output: Does not exist.
Input Value of the Largest Output: x=0
E
e See solution.
Practice makes perfect
a We are asked to find the x-value of the smallest and largest possible output of the given function
y=(x-2)^2
Let's look at its graph!
We can see that the graph is symmetric about x=2. That is also the x-value of the lowest point of the graph. Also, notice that the y-values grow indefinitely.
Therefore, this graph does not have the highest point!
b Let's begin by looking at the graph of the given function.
Notice that the graph is symmetric about x=0. Also, this is the x-value of the lowest point of the graph.
Just like in the previous part, the output values grow indefinitely, and so this graph does not have the highest point!
c We will try to find the x-values of the highest and lowest point of the following function.
y=(x+3)^2
Let's look at the graph of this function.
The graph is symmetric about x=- 3. That is also where we can find the smallest possible output of the function. Also, the y-values of the graph of the function grow indefinitely, and so this graph does not have the highest point!
d Looking at the graph of this function, we can see that the parabola opens downward this time.
We can see that the graph is symmetric about x=0. This is also the x-value of the highest point of the graph. Additionally, we can see that the y-values of the graph decrease indefinitely. This means that the function does not have the smallest output.
e For each of the functions, the highest or lowest point was found at the x-value about which the graph is symmetric.
