함수의 뜻

For the following exercises, use a graphing utility to estimate the local extrema of each function and to estimate the intervals on which the function is increasing and decreasing.

$n(x)={x}^{4}-8{x}^{3}+18{x}^{2}-6x+2$

The graph of the function $f$ is shown in (the referenced figure).

Based on the calculator screen shot, the point $(1.333,\,5.185)$ is which of the following?

• ⓐa relative (local) maximum of the function
• ⓑthe vertex of the function
• ⓒthe absolute maximum of the function
• ⓓa zero of the function

Let $f(x)=\frac{1}{x}.$ Find a number $c$ such that the average rate of change of the function $f$ on the interval $(1,c)$ is $-\frac{1}{4}.$

Let $f(x)=\frac{1}{x}$ . Find the number $b$ such that the average rate of change of $f$ on the interval $(2,b)$ is $-\frac{1}{10}.$

At the start of a trip, the odometer on a car read 21,395. At the end of the trip, 13.5 hours later, the odometer read 22,125. Assume the scale on the odometer is in miles. What is the average speed the car traveled during this trip?

A driver of a car stopped at a gas station to fill up their gas tank. They looked at their watch, and the time read exactly 3:40 p.m. At this time, they started pumping gas into the tank. At exactly 3:44, the tank was full and the driver noticed that they had pumped 10.7 gallons. What is the average rate of flow of the gasoline into the gas tank?

Near the surface of the moon, the distance that an object falls is a function of time. It is given by $d(t)=2.6667{t}^{2},$ where $t$ is in seconds and $d(t)$ is in feet. If an object is dropped from a certain height, find the average velocity of the object from $t=1$ to $t=2.$

The graph in (the referenced figure) illustrates the decay of a radioactive substance over $t$ days.

Use the graph to estimate the average decay rate from $t=5$ to $t=15.$

How do you solve an absolute value equation?

How can you tell whether an absolute value function has two x-intercepts without graphing the function?

When solving an absolute value equation, the isolated absolute value term is equal to a negative number. What does that tell you about the graph of the absolute value function?

How can you use the graph of an absolute value function to determine the x-values for which the function values are negative?

Describe all numbers $x$ that are at a distance of 4 from the number 8. Express this set of numbers using absolute value notation.

Describe all numbers $x$ that are at a distance of $\frac{1}{2}$ from the number −4. Express this set of numbers using absolute value notation.

Describe the situation in which the distance that point $x$ is from 10 is at least 15 units. Express this set of numbers using absolute value notation.

Find all function values $f(x)$ such that the distance from $f(x)$ to the value 8 is less than 0.03 units. Express this set of numbers using absolute value notation.

For the following exercises, find the x- and y-intercepts of the graphs of each function.

$f(x)=4|x-3|+4$

For the following exercises, find the x- and y-intercepts of the graphs of each function.

$f(x)=-3|x-2|-1$

For the following exercises, find the x- and y-intercepts of the graphs of each function.

$f(x)=-2|x+1|+6$

For the following exercises, find the x- and y-intercepts of the graphs of each function.

$f(x)=-5|x+2|+15$