box is made from a piece of cardboard that measures 15 by 9 inches. Squares of equal size will be cut out of each corner. The sides will then be folded up to form a rectangular hat size square should be cut from each comer to obtain maximum volume? with a side of length \( \square \) inches should be cut away from each corner to obtain the maximum volume. to the nearest hundredth as needed.)

When the function \( f(x)=\cos x \) is reflected across the \( x \)-axis, the resulting function is \( g(x)=-\cos x \). If the coordinates of the \( y \)-intercept of \( f(x)=\cos x \) are \( (0,1) \), what are the coordinates of the \( y \)-intercept of the reflected function \( g(x) \) ? (1 point) \( (1,0) \) \( (-1,0) \) \( (0,-1) \) \( (-1,1) \)

Use transformations to graph the function. Determine the domain, range, horizontal asymptote, and \( y \)-intercept of the function. \( f(x)=4^{x}+3 \) Use the graphing tool to graph the function. What is the domain of \( f(x)=4^{x}+3 \) ? (For any answer boxes shown with the grapher, type an exact answer.) (Type your answer in interval notation.)

The table contains values for \( f(x) \). If \( h(x) \) is the reflection of \( f(x) \) across the \( x \)-axis, find the missing value in the ordered pair below, for \( h(x) \). \( x \quad-\frac{\pi}{2}-\frac{\pi}{4} \) \( f(x) \) 0

Let \( f(x)=7\left(\frac{1}{2}\right)^{x} \). Complete parts (a) through (e) below. (e) Is f a one-to-one function? Does fhave an inverse?

Part 2 of 5 A campground owner has 2500 m of fencing. He wants to enclose a rectangular field bordering a river, with no fencing along the river. (See the s 0.71 of 1 (a) Write an expression for the length of the field as a function of \( x \). (b) Find the area of the field (area \( = \) length \( \times \) width) as a function of \( x \). (c) Find the value of \( x \) leading to the maximum area. (d) Find the maximum area. (a) \( \ell(x)=2500-2 x \) (b) \( A(x)= \)