Exam 1: Functions and Graphs

Sketch the graph of y1 as a solid line or curve. Then sketch the graph of y2 as a dashed line or curve by one or more of these: a vertical and/or horizontal shift of the graph y1, a vertical stretch or shrink of the graph of y1, or a reflection of the graph of y1 across an axis. - $y_{1}=x^{3} ; y_{2}=(x+2)^{3}$

Sketch the graph of y1 as a solid line or curve. Then sketch the graph of y2 as a dashed line or curve by one or more of these: a vertical and/or horizontal shift of the graph y1, a vertical stretch or shrink of the graph of y1, or a reflection of the graph of y1 across an axis. -

Write the word or phrase that best completes each statement or answers the question. Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x. - $f ( x ) = 7 x + 4 \text { and } g ( x ) = \frac { x - 4 } { 7 }$

Find the range of the function. - $f ( x ) = 7 x - 5$

Determine whether the graph is the graph of a function. -

Choose the one alternative that best completes the statement or answers the question. Write a mathematical expression for the quantity described verbally. -Eight less than four times a number $x$

Solve the problem. -Sue invested $10,000, part at 5.9% annual interest and the balance at 6.7% annual interest. How much is invested at each rate if a 1-year interest payment is $645.52?

Write the word or phrase that best completes each statement or answers the question. -Graph the function $y = \frac { 1 } { x - 2 }$ in connected mode in the standard viewing window of your calculator. Does your calculator draw a nearly vertical line in the neighborhood of $x = 2$ ? Should this line be present? Why or why not?

Solve the problem. -Estimate graphically the local maximum and local minimum of $f ( x ) = 2 x ^ { 2 } + 3 x + 5$ .

Use an equation to solve the problem. -A tire of a moving bicycle has radius 16 inches. If the tire is making 3 rotations per second, find the bicycle's speed in miles per hour.

Solve the problem. -The speed of a freight train is 23 mph slower than that of a passenger train. The freight train travels 350 mi in the same time it takes the passenger train to travel 440 mi. Find the speed of the passenger train.

Choose the one alternative that best completes the statement or answers the question. Graph the piecewise-defined function. - $f ( x ) = \left\{ \begin{array} { l } x ^ { 2 } \text { if } x < - 1 \\\frac { 1 } { 2 } \text { if } - 1 \leq x < 0 \\\frac { 1 } { 1 + e ^ { - x } } \text { if } x \geq 0\end{array} \right.$

Solve the equation algebraically. - $( x - 12 ) ^ { 2 } = 4$

Solve the problem. -Estimate graphically the local maximum and local minimum of $\mathrm { f } ( \mathrm { x } ) = 0.02 \mathrm { x } ^ { 5 } - 0.04 \mathrm { x } ^ { 4 } - 0.06 \mathrm { x } ^ { 3 } + 1.46 \mathrm { x } ^ { 2 } + 1$ .

Solve the equation algebraically. - $x ^ { 2 } - 7 x - \frac { 1 } { 7 } = 0$

Solve the problem. -Estimate graphically the local maximum and local minimum of $f ( x ) = x \sqrt { x + 2 }$ .

Use an equation to solve the problem. -When a number, half of the number, and a third of the number are added together, the sum is 275 . Find the three numbers.

Determine if the function is one-to-one. -

Solve the equation algebraically. - $x ( 2 x + 3 ) = - 1$

Graph the inverse of the function plotted, on the same set of axes. Use a dashed curve for the inverse. -