Answer:
a. Function; every x-value corresponds to only 1 y-value
b. Not a function; doesn't pass the VLT
c. Function, passes the VLT
2.
a. -200
b. x= -22.5
Explanation:
Here is the basic rule for a function:
Every input (x) value goes only to one output (y) value.
For example, an x-value of 4 cannot go to y-values of both 2 and 4. {(4,2), (4,4)
a.
In a, we see that every x value has only one line- no x-value goes to two different y values, therefore, a is a function.
b. Remember that every x-value can only have one matching y value. This definition allows us to do a special test called the vertical line test (VLT). If we pass a vertical line through a graph (|) and it doesn't pass through two points at the same x value, then that graph is a function.
However, in this graph we can clearly see that this function DOES NOT pass the VLT.
(-2, 2) and (-2,-3)
c.
We're going to use the VLT once again. If we put a vertical line through the observable graph does any x value appear to have two or more y-values? No, so this is the graph of a function
2.
g(x)= 16 -4x
g(54) is the same as saying input 54 in for x, so
16- 4(54)
16- 216 = -200
a. -200
b.
So, g(x) = 106 and they want you to determine x.
Set g(x) equal to 106 and solve:
106= 16-4x
90 = -4x
x= -22.5