All functions have a dependent variable. TRUE
All functions have an independent variable. TRUE
The range of a function includes its domain. FALSE
[Range refers to the set of outputs the function produces, domain the set of inputs the function accepts. They don't really have to have anything to do with each other.]
A vertical line is an example of a functional relationship. FALSE
[For a function, each input (x value) maps to at most one output (y value). A vertical line has lots of ys for a single x.]
A horizontal line is an example of a functional relationship. TRUE
[It's a constant function.]
Each output value of a function can correspond to only one input value. FALSE
[A function can have the same output given different inputs, for example f(x)=x^2 has f(1)=f(-1) ]
3 x + 2 y + z x + y + z , x = 2 , y = 3 , z = 1 tan ( x ) , x = − π 3 x + 2 y + z , x = 2 , y = 3 , z = 1
Answer:
The smaller number is 23
Step-by-step explanation:
Given
Let the odd numbers be x and y [x, being the smallest]
Such that
and
Required
Find x
Substitute in
![x * [x + 2] = 575](https://tex.z-dn.net/?f=x%20%2A%20%5Bx%20%2B%202%5D%20%3D%20575)
Open bracket
Equate to 0
Expand
Factorize
Factor out x + 25
Solve
or 
or 
But x can't be negative.
So:
Answer:
= 1/3
Step-by-step explanation:
= 
if f(x) = y, 
= x, so
= 3 since f(3) = 52
finding f'(3)
f'(x) = 3
f'(3) = 3
= 1/f'(x) = 1/3
