Given the following function, (a) find the vertex; (b) determine whether there is a maximum or a minimum value, and find the value; (c) find the range; and (d) find the intervals on which the function is increasing and the intervals on which the function is decreasing. \( f(x)=3 x^{2}+6 x-45 \) Select the correct choice below and fill in the answer box within your choice. (Type an integer or a fraction.) A. The parabla opens downward and has a maximum value of B. The parabola opens upward and has a minimum value of (c) What is the range of \( f(x) \) ? The range of \( f(x) \) is \( \square \). (Type your answer in interval notation. Use integers or fractions for any numbers in the expression.) (d) On what interval is the function increasing? The function is increasing on \( \square \). (Type your answer in interval notation. Use integers or fractions for any numbers in the expression.)

Let \( f(x)=7\left(\frac{1}{2}\right)^{x} \). Complete parts (a) through (e) below (c) Find any asymptotes of the graph of \( f \). Select the co

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) \( (1,0) \) \( (-1,0) \) \( (0,-1) \) \( (-1,1) \)

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) \( A(x)= \)

1. Write the following sets as an interval or union of interval. In each case \( x \in \Re \). a) \( A=\{x: x \neq 0 \wedge x \neq 8\} \) b) \( B=\left\{x: x^{2}\left(x^{2}-1\right) \neq 0\right\} \) c) \( B=\left\{x: x^{2}=2 \Leftrightarrow x \geq-1\right\} \) d) \( C=\left\{x:\left(x^{3}-2 x\right) \neq 0\right\} \) e) \( C=\{x:(x-2)(x+3)=0 \Rightarrow x \geq 0\} \)

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