Problem 99
Question
Begin by graphing the standard cubic function, \(f(x)=x^{3} .\) Then use transformations of this graph to graph the given function. $$h(x)=-x^{3}$$
Step-by-Step Solution
Verified Answer
The graph of \(h(x)=-x^3\) is the reflection of the graph of \(f(x)=x^3\) over the x-axis, resulting in an inverted curvy 'S' shape in the second and fourth quadrants.
1Step 1: Graph the standard cubic function
Start by graphing the standard cubic function \(f(x)=x^3\). This function looks like a curvy 'S' in the first and third quadrants. The highest and lowest points in the graph don't have any bounds.
2Step 2: Understand the given transformation
The aim is to graph the function \(h(x) = -x^3\). The negative sign in front of \(x^3\) is a reflection over the x-axis according to function transformations
3Step 3: Apply transformations to graph the given function
Reflect the graph of \(f(x)=x^3\) over the x-axis to graph \(h(x)=-x^3\). This means every point \((a, b)\) on the graph of \(f(x)=x^3\) will become \((a, -b)\) on the graph of \(h(x)=-x^3\). This will result in an inverted curvy 'S' that is in the second and fourth quadrants.
Other exercises in this chapter
Problem 99
A company that sells radios has yearly fixed costs of \(\$ 600,000 .\) It costs the company \(\$ 45\) to produce each radio. Each radio will sell for \(\$ 65 .\
View solution Problem 99
In Tom Stoppard's play Arcadia, the characters dream and talk about mathematics, including ideas involving graphing, composite functions, symmetry, and lack of
View solution Problem 100
Solve: \(\frac{2}{x+3}-\frac{4}{x+5}=\frac{6}{x^{2}+8 x+15}\) (Section P.7, Example 3)
View solution Problem 100
A department store has two locations in a city. From 2012 through \(2016,\) the profits for each of the store's two branches are modeled by the functions \(f(x)
View solution