함수 전체 문제

For the following exercises, use a calculator to find the answer.

Graph on the same set of axes the functions $f(x)={x}^{2}$, $f(x)=2{x}^{2}$, and $f(x)=\frac{1}{3}{x}^{2}$.

What appears to be the effect of changing the coefficient?

For the following exercises, use a calculator to find the answer.

Graph on the same set of axes $f(x)={x}^{2},f(x)={x}^{2}+2$ and $f(x)={x}^{2},f(x)={x}^{2}+5$ and $f(x)={x}^{2}-3.$ What appears to be the effect of adding a constant?

For the following exercises, use a calculator to find the answer.

Graph on the same set of axes $f(x)={x}^{2},f(x)={(x-2)}^{2},f{(x-3)}^{2}$, and $f(x)={(x+4)}^{2}.$

What appears to be the effect of adding or subtracting those numbers?

For the following exercises, use a calculator to find the answer.

The path of an object projected at a 45 degree angle with initial velocity of 80 feet per second is given by the function $h(x)=\frac{-32}{{(80)}^{2}}{x}^{2}+x$ where $x$ is the horizontal distance traveled and $h(x)$ is the height in feet. Use the TRACE feature of your calculator to determine the height of the object when it has traveled 100 feet away horizontally.

For the following exercises, use a calculator to find the answer.

A suspension bridge can be modeled by the quadratic function $h(x)=.0001{x}^{2}$ with $-2000\le x\le 2000$ where $|x|$ is the number of feet from the center and $h(x)$ is height in feet. Use the TRACE feature of your calculator to estimate how far from the center does the bridge have a height of 100 feet.

For the following exercises, use the vertex of the graph of the quadratic function and the direction the graph opens to find the domain and range of the function.

Vertex $(1,-2),$ opens up.

For the following exercises, use the vertex of the graph of the quadratic function and the direction the graph opens to find the domain and range of the function.

Vertex $(-1,2)$ opens down.

For the following exercises, use the vertex of the graph of the quadratic function and the direction the graph opens to find the domain and range of the function.

Vertex $(-5,11),$ opens down.

For the following exercises, use the vertex of the graph of the quadratic function and the direction the graph opens to find the domain and range of the function.

Vertex $(-100,100),$ opens up.

For the following exercises, write the equation of the quadratic function that contains the given point and has the same shape as the given function.

Contains $(1,1)$ and has shape of $f(x)=2{x}^{2}.$ Vertex is on the $y-$ axis.

For the following exercises, write the equation of the quadratic function that contains the given point and has the same shape as the given function.

Contains $(-1,4)$ and has the shape of $f(x)=2{x}^{2}.$ Vertex is on the $y-$ axis.

For the following exercises, write the equation of the quadratic function that contains the given point and has the same shape as the given function.

Contains $(2,3)$ and has the shape of $f(x)=3{x}^{2}.$ Vertex is on the $y-$ axis.

For the following exercises, write the equation of the quadratic function that contains the given point and has the same shape as the given function.

Contains $(1,-3)$ and has the shape of $f(x)=-{x}^{2}.$ Vertex is on the $y-$ axis.

For the following exercises, write the equation of the quadratic function that contains the given point and has the same shape as the given function.

Contains $(4,3)$ and has the shape of $f(x)=5{x}^{2}.$ Vertex is on the $y-$ axis.

For the following exercises, write the equation of the quadratic function that contains the given point and has the same shape as the given function.

Contains $(1,-6)$ has the shape of $f(x)=3{x}^{2}.$ Vertex has x-coordinate of $-1.$

Among all of the pairs of numbers whose sum is 6, find the pair with the largest product. What is the product?

Among all of the pairs of numbers whose difference is 12, find the pair with the smallest product. What is the product?

Suppose that the price per unit in dollars of a cell phone production is modeled by $p=\text{\textdollar}45-0.0125x,$ where $x$ is in thousands of phones produced, and the revenue represented by thousands of dollars is $R=x\cdot p.$ Find the production level that will maximize revenue.

A soccer stadium holds 62,000 spectators. With a ticket price of $11, the average attendance has been 26,000. When the price dropped to $9, the average attendance rose to 31,000. Assuming that attendance is linearly related to ticket price, what ticket price would maximize revenue?

A farmer finds that if she plants 75 trees per acre, each tree will yield 20 bushels of fruit. She estimates that for each additional tree planted per acre, the yield of each tree will decrease by 3 bushels. How many trees should she plant per acre to maximize her harvest?