0. Functions

Evaluating functions from graphs Assume ƒ is an odd function and that both ƒ and g are one-to-one. Use the (incomplete) graph of ƒ and g the graph of to find the following function values. <IMAGE>

ƒ(g(4))

Evaluate the triple integral ${\int }_{}^{}{\int }_{}^{}{\int }_{}^{}z{d}_V$, where E is the region bounded by the parabolic cylinder $y=x^2$, the planes $z=0$, $z=4$, and $y=4$.

Which of the following best describes the contour lines (level curves) of the function $f(x,y)=x^2+7y^2$?

Consider the function $z=e^x\cos \left(y\right)$. Which of the following best describes the domain of this function?

If $f\left(x\right)=2x^2+1$, what is the value of $f\left(3\right)$?

Given the function $f\left(x\right)=x^2$ defined on the interval $0\le x\le 2$, determine the y-coordinate of the centroid of the region bounded by the graph of $f\left(x\right)$, the x-axis, and the lines $x=0$ and $x=2$.

Find the third-degree Taylor polynomial, $t_3\left(x\right)$, for the function $f\left(x\right)=\frac{1}{x}$ centered at $a=2$.

In Exercises 19–32, find the (a) domain and (b) range.

𝔂 = 4 sin ( 1 )

x

Decide whether $f$, $g$, or both represent one-to-one functions. <IMAGE>

Given the Laplace transform $F\left(s\right)=\frac{1}{s^2+1}$, find the corresponding function $f\left(t\right)$.

If $f\left(x\right)=x^3$, which of the following is the value of $f(-2)$?

Let $g\left(x\right)={\int }_0^{x}f\left(t\right)dt$, where $f$ is the function whose graph is shown. Which of the following statements is true about $g\left(x\right)$?

Average single-family home prices P (in thousands of dollars) in Sacramento, California, are shown in the accompanying figure from the beginning of 2006 through the end of 2015.

b. Estimate home prices at the end of

i) 2007 ii) 2012 iii) 2015

Given the sphere defined by the equation $x^2+y^2+z^2=9$, what is the intersection of this sphere with the yz-plane?

Find the exact length of the curve $y=\frac{1}{4}{x}^2-\frac{1}{2}\ln \left(x\right)$ for $1\le x\le 4$.