Hi there!
The range of a function describes its possible y-values. For example, y=x produces a linear graph. Its range is all real numbers, meaning that for any value of y, the function is defined.
However, for y=x², for example, the range is y>0, since there the graph doesn't travel to y-values less than 0. The function is only defined when y>0.
To find the range of the given functions, you can try graphing them. Or, if you've memorized the ranges of their parent functions, you can try to take that and apply transformations.
Answer for the first question:
f(x)=-√x
The parent function is f(x)=√x. The range of this is y≥0.
f(x)=-√x
Adding a negative in front of the square root reflects the function across the x-axis, meaning the range is therefore flipped too:
y≤0
I hope this helps!
Answer:
116
Step-by-step explanation:
V = 25^3
Since a cube has equal lengths on each side, you multiply the 25 by itself three times to get:
V = 15,625cm^3
A:
So terms are a group of numbers/variables or a single number/variable. They are separated by + and - symbols.
In the original equation, there are 6 terms: 5x^2, 6x, -3, 4x^2, -8x, and 2.
To find the simplified equation, just combine like terms, which in this case are (5x^2 + 4x^2) + (6x - 8x) + (-3 + 2).
Simplify that, and your simplified equation is 9x^2 - 2x - 1 . And within this simplified equation, there are 3 terms: 9x^2, -2x, and -1.
B:
Going back to A, we see that our simplified expression is 9x^2 - 2x - 1 . Looking at our equation, the coefficient of x is -2.
Answer:
(g°f)x =16 when x = 5
Step-by-step explanation:
It might be easier to understand if you wrote this the other acceptable way.
g(x) = x^4
f(x) = 2x - 8
g(f(x)) means that in g(x) wherever you see and x you put f(x)
g(f(x)) = (f(x) ) ^ 4 Now put in the general value for f(x)
g(2x - 8) = (2x - 8)^4
You really don't want to expand this (although it would give you the right answer eventually).
g(2*5 - 8) = (2 * 5 - 8)^4
g(2*5 - 8) = (10 - 8)^4
g(2*5 - 8) = 2^4
Answer 16
