Answer:
1: B
2: H
3. C or D (it's hard to tell, especially without an equation)
4. J
5. A
6. G
7. B
Step-by-step explanation:
1:
f(x) - g(x)
(x^2 + 8x) - (3x - 5) Distribute the negative
x^2 + 8x - 3x + 5 Combine like terms
x^2 + 5x + 5
2:
f(g(x))
Plug g(x) into f(x)
(2x - 1)^2 - 3
Immediately we can see that there will be a 4x^2 (because 2x times 2x = 4x^2) so we know the answer will be H because that's the only option with 4x^2
3:
The line starts at -4 on the x axis and goes infinitely to the right so everything greater than (and maybe equal to) -4.
On the y axis, the line starts at 0 and goes infinitely up so everything greater than (and maybe equal to) 0.
4:
To find the inverse of a function:
<em>f(x) -> y</em>
<em>Switch x and y</em>
<em>Solve for y again</em>
x = 3 +5y
x-3 = 5y
(x-3)/5 = y
5:
If option A were inverse functions, h(x) would be
x = 2y + 9
x - 9 = 2y
(x-9)/2 = y
Which could also be written as (1/2)x - 9/2 or (1/2)x - 4.5 but not (1/2)x - 9
6:
As y approaches -1, x approaches 1. Going the other direction,
As y approaches positive infinity, x approaches positive infinity.
7:
The number inside directly affecting the x moves the function left and right (left is positive, right is negative). The number outside moves the function up and down. So (x + 4) moves it left 4 and the +1 moves it up 1.
