3. Functions

Intro to Functions & Their Graphs

Open Question
In Exercises 89–90, express the given function h as a composition of two functions f and g so that h(x) = (f ○ g)(x). h(x) = (x^2 + 2x - 1)^4
Open Question
In Exercises 91–94, use the graphs of f and g to evaluate each composite function.
(fog) (-1)
Multiple Choice
State the inputs and outputs of the following relation. Is it a function? { $\left(-3,5\right),\left(0,2\right),\left(3,5\right)$ }
Multiple Choice
State the inputs and outputs of the following relation. Is it a function? { $\left(2,5\right),\left(0,2\right),\left(2,9\right)$ }
Multiple Choice
Is the equation $y=-2x+10$ a function? If so, rewrite it in function notation and evaluate at $f\left(3\right)$ .
Multiple Choice
Is the equation $y^2+2x=10$ a function? If so, rewrite it in function notation and evaluate at $f\left(-1\right)$ .
Multiple Choice
Find the domain and range of the following graph (write your answer using interval notation).
Multiple Choice
Find the domain of $f\left(x\right)=\sqrt{x+4}$ . Express your answer using interval notation.
Multiple Choice
Find the domain of $f\left(x\right)=\frac{1}{x^2-5x+6}$ . Express your answer using interval notation.
Open Question
In Exercises 1–30, find the domain of each function. f(x)=3(x-4)
Open Question
Without using paper and pencil, evaluate each expression given the following functions. ƒ(x)=x+1 and g(x)=x^2(ƒ-g)(2)
Open Question
Without using paper and pencil, evaluate each expression given the following functions. ƒ(x)=x+1 and g(x)=x^2(ƒ∘g)(2)
Open Question
In Exercises 1–30, find the domain of each function. g(x) = 3/(x^2-2x-15)
Open Question
In Exercises 1–30, find the domain of each function. f(x) = 1/(x+7) + 3/(x-9)
Open Question
Let ƒ(x)=x^2+3 and g(x)=-2x+6. Find each of the following. See Example 1. (ƒ+g)(-5)