Advanced Pre Calculus Review (1)

Consider the quadratic parent function f (x) = $$x^2$$ . Which of the following graphs represents the function f vertically stretched by a factor of 2, reflected across the x-axis, and shifted down two units?

The graph of $$g\left(x\right)\ =-2\left(x+1\right)^3$$ can be obtained from the graph of $$f\left(x\right)=x^3$$ , the cubic parent function, by applying which of the following transfo1mations?

If P(3,5) is a point on the graph of y = f (x), identify the corresponding point on the graph of $$y=f\left(x-1\right)+7$$

What is the inverse of $$f\left(x\right)=\sqrt[2]{-2x+6}$$ ?

If $$f\left(x\right)=\sqrt[2]{2x+1}$$ , then the inverse function is

If j(x)= $$f^{-1}\left(x\right)$$ , then j(2)=

If h(x) =f(g(x)), then h(3) =

Let f and g be the functions defined by f(x) = $$x^2+1$$ and g(x) = $$\sqrt[2]{x-2}$$ . Which of the following represents the equation of h(x)= (f o g)(x)?

Which of the following graphs represents the polynomial $$f\left(x\right)=-\left(x-2\right)\left(x-1\right)^2\left(x+1\right)$$ ?

Let f be a polynomial function defined as $$f\left(x\right)=x\left(x-1\right)\left(x+1\right)^2$$ . Which of the following statements is true?

I. The degree of f is 4.

II. f has at least 4 real zeros.

III. The graph of f crosses the x-axis at x=-1