Use transformations of the graph of \( f(x)=2^{x} \) 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. \( h(x)=2^{x-2}-1 \) Graph \( h(x)=2^{x-2}-1 \) and its asymptote. Graph the asymptote as a dashed line. Use the graphing tool to graph the function.

(a) Express the distance \( d \) from \( P \) to the origin as a function of \( x \). \( d(x)=\sqrt{\mathrm{x}^{4}-3 \mathrm{x}^{2}+4} \) (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 (Type an integer or decimal rounded to two decimal places as needed.)

Find the function that is finally graphed after the following transformations are applied to the graph of \( y=\sqrt{x} \) in the order listed. (1) Shift up 7 units (2) Reflect about the \( x \)-axis (3) Reflect about the \( y \)-axis \( y= \)

Given the function with the equation \( k(x)=\frac{-6}{x+2}-2 \) : \( 7.1 \quad \) Write the equations of the asymptotes of \( k \).

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 \( y=f(x) \).

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