Begin by graphing \( f(x)=3^{x} \). Then use transformations of this graph to graph the given function. Be sure to graph and give the equation of the asymptote. Use the graph to determine the function's domain and range. If applicable, use a graphing utility to confirm your hand-drawn graphs. \( g(x)=3^{x}-1 \) B. The graph of \( f(x)=3^{x} \) should be shifted 1 unit upward. C. The graph of \( f(x)=3^{x} \) should be shifted 1 unit to the right. Graph \( g(x)=3^{x}-1 \) and its asymptote. Use the graphing tool to graph the function as a \( f(x)=3^{x} \) should be shifted 1 unit downward. solid curve and the asymptote as a dashed line. The equation of the asymptote for \( g(x)=3^{x}-1 \) is The . (Type an equation.)

Given: \( f(x)=2\left(x^{2}-1\right) \) Sketch function \( f \) on the diagram sheet. Clearly show all intercepts with the axes.

(a) Express the distance \( d \) from \( P \) to the origin as a function of \( x \). \( d(x)=\sqrt{x^{4}-3 x^{2}+4} \) (Simplify your answer. Type an exact answer, using radicals as needed.) (b) What is \( d \) if \( x=0 \) ? If \( x=0 \), the distance \( d \) is 2 . (Type an integer or decimal rounded to two decimal placels as needed.) (c) What is \( d \) if \( x=1 \) ? If \( x=1 \), the distance \( d \) is \( \square \). (Type an integer or decimal rounded to two decimal places as needed.)

Let \( P=(x, y) \) be a point on the graph of \( y=x^{2}-2 \). Complete parts (a) through (e) below. (a) Express the distance \( d \) from \( P \) to the origin as a function of \( x \). \( d(x)= \) (Simplify your answer. Type an exact answer, using radicals as needed.)

Given \( f(x)=\frac{-2}{x}-2 \), Answer the following questions: .1 Write down the equations of the asymptotes of \( f(x) \). 2 Draw a neat sketch graph of \( f(x) \), clearly indicate the asymptotes and the intercepts with the axes. .3 Write down the domain and range of \( f(x) \).

Complete the sentence below. Suppose that the graph of a function \( f \) is known. Then the graph of \( y=f(-x) \) may be obtained by a reflection about the -axis of the graph of the function \( y=f(x) \). Suppose that the graph of a function \( f \) is known. Then the graph of \( y=f(-x) \) may be obtained by a reflection about the -axis of the graph of the function \( y=f(x) \).