Functions and Graphs


Express the area and circumference of a circle as functions of the circle’s radius. Then express the area as a function of the circumference.

A GPS device tracks the elevation $E$ (in feet) of a hiker walking in the mountains. The elevation $t$ hours after beginning the hike is given in the figure. <IMAGE>

Notice that the curve in the figure is horizontal for an interval of time near $t=5.5$ hr. Give a plausible explanation for the horizontal line segment.

In each exercise, a function and an interval of its independent variable are given. The endpoints of the interval are associated with points $P$ and $Q$ on the graph of the function.

a. Sketch a graph of the function and the secant line through $P$ and $Q$.

b. Find the slope of the secant line in part (a), and interpret your answer in terms of an average rate of change over the interval. Include units in your answer.

After $t$ seconds, an object dropped from rest falls a distance $d=16t^2$, where $d$ is measured in feet and $2\leq{t}\leq{5}$.

{Use of Tech} A family of superexponential functions Let ƒ(x) = (a + x)ˣ , where a > 0.

a. What is the domain of f (in terms of a)?

{Use of Tech} A family of superexponential functions Let ƒ(x) = (a + x)ˣ , where a > 0.

b. Describe the end behavior of f (near the left boundary of its domain and as x→∞).

Express the radius of a sphere as a function of the sphere’s surface area. Then express the surface area as a function of the volume.

Horizontal and Vertical Asymptotes

Determine the domain and range of y = (√16―x²) / (x―2).

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

𝔂 = |x| - 2

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

____

𝔂 = -2 + √1 - x