Write a function based on the given parent function and transformations in the given order. Parent function: y = x³ Shift 4.2 units to the left. Reflect across the y-axis. Shift upward 2.3 units.

Write a function based on the given parent function and transformations in the given order. Parent function: y = x³ Shift 4.2 units to the left. Reflect across the y-axis. Shift upward 2.3 units.

Question
Functions
asked 2021-03-05
Write a function based on the given parent function and transformations in the given order. Parent function: y = x³
Shift 4.2 units to the left. Reflect across the y-axis. Shift upward 2.3 units.

Answers (1)

2021-03-06
Shift 4.2 units to the left: Add 4.2 to the input x: \(\displaystyle{y}={\left({x}+{4.2}\right)}^{{{3}}}\)
Reflect across the yy-axis: Change the sign of x: \(\displaystyle{y}={\left(−{x}+{4.2}\right)}^{{{3}}}\)
Shift upward 2.3 units: Add 2.3 to the output: \(\displaystyle{y}={\left(−{x}+{4.2}\right)}^{{{3}+{2.3}}}\)
0

Relevant Questions

asked 2020-11-27
Starting with the function \(f(x) = e^x\), create a new function by performing the following transformations.
i. First shift the graph of f (x) to the left by two units.
\(f_1 (x) =\)?
ii. Then compress your result by a factor of \(1/7\)
\(f_2 (x) =\) ?
iii. Next, reflect it across the x-axis.
\(f_3 (x) =\) ?
iv. And finally shift it up by eight units to create g (x).
g (x) =?
asked 2021-05-19
Consider the function \(f(x)=2x^{3}-6x^{2}-18x+9\) on the interval [-2,4].
What is the absolute minimum of f(x) on [-2,4]?
What is the absolute maximum of f(x) on [-2,4]?
asked 2021-05-09
Find the absolute maximum and absolute minimum values of f on the given interval.
\(f(x)=x+\frac{4}{x},[0.2,8]\)
asked 2021-06-07
Find the absolute maximum and absolute minimum values of f on the given interval.
\(f(x)=5+54x-2x^{3}, [0,4]\)
asked 2021-02-14
Dayton Power and Light, Inc., has a power plant on the Miami Riverwhere the river is 800 ft wide. To lay a new cable from the plantto a location in the city 2 mi downstream on the opposite sidecosts $180 per foot across the river and $100 per foot along theland.
(a) Suppose that the cable goes from the plant to a point Q on theopposite side that is x ft from the point P directly opposite theplant. Write a function C(x) that gives the cost of laying thecable in terms of the distance x.
(b) Generate a table of values to determin if the least expensivelocation for point Q is less than 2000 ft or greater than 2000 ftfrom point P.
asked 2021-05-12
Find the absolute maximum and absolute minimum values of f on the given interval and state where those values occur: \(f(x)=x^{3}-3x^{2}-9x+25, [-5,10]\)
asked 2021-05-09
Find the absolute maximum and minimum values of f on the given interval.
\(f(x)=4x^{3}-6x^{2}-24x+9. [-2,3]\)
asked 2021-06-01
Consider the function \(f(x)=2x^{3}+6x^{2}-90x+8, [-5,4]\)
find the absolute minimum value of this function.
find the absolute maximum value of this function.
asked 2021-04-21
The crane shown in the drawing is lifting a 182-kg crate upward with an acceleration of \(\displaystyle{1.5}\frac{{m}}{{s}^{{2}}}\). The cable from the crate passes over a solid cylindrical pulley at the top of the boom. The pulley has a mass of 130 kg. The cable is then wound ontoa hollow cylindrical drum that is mounted on the deck of the crane.The mass of the drum is 150 kg, and its radius is 0.76 m. The engine applies a counter clockwise torque to the drum in order towind up the cable. What is the magnitude of this torque? Ignore the mass of the cable.
asked 2021-03-20
The graph of y = f(x) contains the point (0,2), \(\displaystyle{\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}}={\frac{{-{x}}}{{{y}{e}^{{{x}^{{2}}}}}}}\), and f(x) is greater than 0 for all x, then f(x)=
A) \(\displaystyle{3}+{e}^{{-{x}^{{2}}}}\)
B) \(\displaystyle\sqrt{{{3}}}+{e}^{{-{x}}}\)
C) \(\displaystyle{1}+{e}^{{-{x}}}\)
D) \(\displaystyle\sqrt{{{3}+{e}^{{-{x}^{{2}}}}}}\)
E) \(\displaystyle\sqrt{{{3}+{e}^{{{x}^{{2}}}}}}\)
...