Chapter 1

Draw the angle using a ray through the origin, and determine whether the sine, cosine, and tangent of that angle are positive, negative, zero, or undefined. $$\frac{3 \pi}{2}$$

the function continuous on the interval? $$\frac{1}{x-2} \text { on }[-1,1]$$

For Exercises \(1-2,\) what happens to the value of the function as \(x \rightarrow \infty\) and as \(x \rightarrow-\infty ?\) $$y=0.25 x^{3}+3$$

Simplify the expressions completely. $$e^{\ln (1 / 2)}$$

The population of a city, \(P\), in millions, is a function of \(t,\) the number of years since \(1970,\) so \(P=f(t) .\) Explain the meaning of the statement \(f(35)=12\) in terms of the population of this city.

Draw the angle using a ray through the origin, and determine whether the sine, cosine, and tangent of that angle are positive, negative, zero, or undefined. $$2 \pi$$

For Exercises \(1-2,\) what happens to the value of the function as \(x \rightarrow \infty\) and as \(x \rightarrow-\infty ?\) $$y=2 \cdot 10^{4 x}$$

Simplify the expressions completely. $$10^{\log (A B)}$$

The pollutant PCB (polychlorinated biphenyl) affects the thickness of pelican eggs. Thinking of the thickness, \(T\) of the eggs, in \(\mathrm{mm}\), as a function of the concentration, \(P\) of \(\mathrm{PCBs}\) in ppm (parts per million), we have \(T=f(P)\) Explain the meaning of \(f(200)\) in terms of thickness of pelican eggs and concentration of PCBs.

Draw the angle using a ray through the origin, and determine whether the sine, cosine, and tangent of that angle are positive, negative, zero, or undefined. $$\frac{\pi}{4}$$

In Exercises \(3-10\), determine the end behavior of each function as \(x \rightarrow+\infty\) and as \(x \rightarrow-\infty\). $$f(x)=-10 x^{4}$$

the function continuous on the interval? $$\frac{1}{\sqrt{2 x-5}} \text { on }[3,4]$$

Simplify the expressions completely. $$5 e^{\ln \left(A^{2}\right)}$$

In Exercises \(4-9,\) draw a possible graph of \(f(x) .\) Assume \(f(x)\) is defined and continuous for all real \(x\). $$\lim _{x \rightarrow \infty} f(x)=-\infty \quad \text { and } \quad \lim _{x \rightarrow-\infty} f(x)=-\infty$$

Draw the angle using a ray through the origin, and determine whether the sine, cosine, and tangent of that angle are positive, negative, zero, or undefined. $$3 \pi$$

In Exercises \(3-10\), determine the end behavior of each function as \(x \rightarrow+\infty\) and as \(x \rightarrow-\infty\). $$f(x)=3 x^{5}$$

the function continuous on the interval? $$\frac{x}{x^{2}+2} \text { on }[-2,2]$$

Find an equation for the line that passes through the given points. $$(0,0) \text { and }(1,1)$$

Simplify the expressions completely. $$\ln \left(e^{2 A B}\right)$$

In Exercises \(4-9,\) draw a possible graph of \(f(x) .\) Assume \(f(x)\) is defined and continuous for all real \(x\). $$\lim _{x \rightarrow \infty} f(x)=-\infty \quad \text { and } \quad \lim _{x \rightarrow-\infty} f(x)=+\infty$$

Draw the angle using a ray through the origin, and determine whether the sine, cosine, and tangent of that angle are positive, negative, zero, or undefined. $$\frac{\pi}{6}$$

Represent exponential growth or decay. What is the initial quantity? What is the growth rate? State if the growth rate is continuous. $$P=5(1.07)^{t}$$

In Exercises \(3-10\), determine the end behavior of each function as \(x \rightarrow+\infty\) and as \(x \rightarrow-\infty\). $$f(x)=5 x^{4}-25 x^{3}-62 x^{2}+5 x+300$$

the function continuous on the interval? $$2 x+x^{2 / 3} \text { on }[-1,1]$$

Find an equation for the line that passes through the given points. $$(0,2) \text { and }(2,3)$$

Simplify the expressions completely. $$\ln (1 / e)+\ln (A B)$$

In Exercises \(4-9,\) draw a possible graph of \(f(x) .\) Assume \(f(x)\) is defined and continuous for all real \(x\). $$\lim _{x \rightarrow \infty} f(x)=1 \quad \text { and } \quad \lim _{x \rightarrow-\infty} f(x)=+\infty$$

Draw the angle using a ray through the origin, and determine whether the sine, cosine, and tangent of that angle are positive, negative, zero, or undefined. $$\frac{4 \pi}{3}$$

Represent exponential growth or decay. What is the initial quantity? What is the growth rate? State if the growth rate is continuous. $$P=7.7(0.92)^{t}$$

In Exercises \(3-10\), determine the end behavior of each function as \(x \rightarrow+\infty\) and as \(x \rightarrow-\infty\). $$f(x)=1000-38 x+50 x^{2}-5 x^{3}$$

Find an equation for the line that passes through the given points. $$(-2,1) \text { and }(2,3)$$

Simplify the expressions completely. $$2 \ln \left(e^{A}\right)+3 \ln B^{e}$$

In Exercises \(4-9,\) draw a possible graph of \(f(x) .\) Assume \(f(x)\) is defined and continuous for all real \(x\). $$\lim _{x \rightarrow \infty} f(x)=-\infty \quad \text { and } \quad \lim _{x \rightarrow-\infty} f(x)=3$$

Draw the angle using a ray through the origin, and determine whether the sine, cosine, and tangent of that angle are positive, negative, zero, or undefined. $$\frac{-4 \pi}{3}$$

Represent exponential growth or decay. What is the initial quantity? What is the growth rate? State if the growth rate is continuous. $$P=3.2 e^{0.03 t}$$

In Exercises \(3-10\), determine the end behavior of each function as \(x \rightarrow+\infty\) and as \(x \rightarrow-\infty\). $$f(x)=\frac{3 x^{2}+5 x+6}{x^{2}-4}$$

Find an equation for the line that passes through the given points. $$(-1,0) \text { and }(2,6)$$

Solve for \(x\) using logs. $$3^{x}=11$$

In Exercises \(3-10\), determine the end behavior of each function as \(x \rightarrow+\infty\) and as \(x \rightarrow-\infty\). $$f(x)=\frac{10+5 x^{2}-3 x^{3}}{2 x^{3}-4 x+12}$$

Represent exponential growth or decay. What is the initial quantity? What is the growth rate? State if the growth rate is continuous. $$P=15 e^{-0.06 t}$$

the function continuous on the interval? $$\frac{1}{\sin x} \text { on }\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$$

For the functions \(f\) and \(g\) find (a) \(f(g(1))\) (b) \(g(f(1))\) (c) \(f(g(x))\) (d) \(g(f(x))\) (e) \(f(t) g(t)\) $$f(x)=x^{2}, g(x)=x+1$$

Determine the slope and the \(y\) -intercept of the line whose equation is given. $$2 y+5 x-8=0$$

Solve for \(x\) using logs. $$17^{x}=2$$

In Exercises \(4-9,\) draw a possible graph of \(f(x) .\) Assume \(f(x)\) is defined and continuous for all real \(x\). $$\lim _{x \rightarrow 3} f(x)=5 \quad \text { and } \quad \lim _{x \rightarrow-\infty} f(x)=+\infty$$

Write the functions in the form \(P=P_{0} a^{t}\) Which represent exponential growth and which represent exponential decay? $$P=15 e^{0.25 t}$$

In Exercises \(3-10\), determine the end behavior of each function as \(x \rightarrow+\infty\) and as \(x \rightarrow-\infty\). $$f(x)=3 x^{-4}$$

the function continuous on the interval? $$\frac{e^{x}}{e^{x}-1} \text { on }[-1,1]$$

For the functions \(f\) and \(g\) find (a) \(f(g(1))\) (b) \(g(f(1))\) (c) \(f(g(x))\) (d) \(g(f(x))\) (e) \(f(t) g(t)\) $$f(x)=\sqrt{x+4}, g(x)=x^{2}$$

Determine the slope and the \(y\) -intercept of the line whose equation is given. $$7 y+12 x-2=0$$