3. Functions

Solve and check: (x-1)/5 - (x+3)/2 = 1- x/4

Express the given function h as a composition of two functions f and g so that h(x) = (f ○ g)(x). h(x) = (x² + 2x - 1)⁴

Use the graphs of f and g to evaluate each composite function.

(fog) (-1)

Determine whether the three points are the vertices of a right triangle. (-4,3),(2,5),(-1,-6)

Complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. x² + y² - 6y -7=0

State the inputs and outputs of the following relation. Is it a function? {$\left(-3,5\right),\left(0,2\right),\left(3,5\right)$}

State the inputs and outputs of the following relation. Is it a function? {$\left(2,5\right),\left(0,2\right),\left(2,9\right)$}

Is the equation $y=-2x+10$ a function? If so, rewrite it in function notation and evaluate at $f\left(3\right)$.

Is the equation $y^2+2x=10$ a function? If so, rewrite it in function notation and evaluate at $f\left(-1\right)$.

Find the domain and range of the following graph (write your answer using interval notation).

Find the domain of $f\left(x\right)=\sqrt{x+4}$ . Express your answer using interval notation.

Find the domain of $f\left(x\right)=\frac{1}{x^2-5x+6}$ . Express your answer using interval notation.