Question

asked 2021-01-19

Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions and then applying the appropriate transformations.

\(y=sqrt(x - 2) - 1\)

\(y=sqrt(x - 2) - 1\)

asked 2021-01-23

Sketch the graph of the function \(f(x) = -2^x+1 +3\) using transformations. Do not create a table of values and plot points

asked 2021-02-11

Your friend attempted to describe the transformations applied to the graph of \(y=sinx\) to give the equation \(f(x)=1/2sin(-1/3(x+30))+1\).

They think the following transformations have been applied. Which transformations have been identified correctly, and which have not? Justify your answer.

a) f(x) has been reflected vertically.

b) f(x) has been stretched vertically by a factor of 2.

c) f(x) has been stretched horizontally by a factor of 3.

d) f(x) has a phase shift left 30 degrees.

e) f(x) has been translated up 1 unit.

They think the following transformations have been applied. Which transformations have been identified correctly, and which have not? Justify your answer.

a) f(x) has been reflected vertically.

b) f(x) has been stretched vertically by a factor of 2.

c) f(x) has been stretched horizontally by a factor of 3.

d) f(x) has a phase shift left 30 degrees.

e) f(x) has been translated up 1 unit.

asked 2021-02-05

Create a new function in the form \(y = a(x- h)^2 + k\) by performing the following transformations on \(f (x) = x^2\)

Give the coordinates of the vertex for the new parabola.

h(x) is f (x) shifted right 3 units, stretched by a factor of 9, and shifted up by 7 units. h(x) = ?

Edit Coordinates of the vertex for the new parabola are:

x=?

y =?

Give the coordinates of the vertex for the new parabola.

h(x) is f (x) shifted right 3 units, stretched by a factor of 9, and shifted up by 7 units. h(x) = ?

Edit Coordinates of the vertex for the new parabola are:

x=?

y =?

asked 2021-01-15

Create a new function in the form \(y = a(x-h)^2 + k\) by performing the following transformations on \(f (x) = x^2\).

Give the coordinates of the vertex for the new parabola.

g(x) is f (x) shifted right 7 units, stretched by a factor of 9, and then shifted down by 3 units. g(x) = ?

Coordinates of the vertex for the new parabola are:

x=?

y=?

Give the coordinates of the vertex for the new parabola.

g(x) is f (x) shifted right 7 units, stretched by a factor of 9, and then shifted down by 3 units. g(x) = ?

Coordinates of the vertex for the new parabola are:

x=?

y=?

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) =?

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 2020-12-12

Explain how you could graph each function by applying transformations.

(a) \(y = log(x -2) + 7\) (b) \(y = -3logx\) (c) \(y = log(-3x)-5\)

(a) \(y = log(x -2) + 7\) (b) \(y = -3logx\) (c) \(y = log(-3x)-5\)

asked 2021-03-18

\(f(x)= (-1)/(3(x+1))+1\)

Domain and range?

Transformations?

Name of Graph?

Domain and range?

Transformations?

Name of Graph?

asked 2021-02-21

Answer the questions and complete the following problems about transformations.
1. In a rotation of a set of points, what geometric structure defines the motion of points?

asked 2021-02-23

List a sequence of transformations, in words, to convert the graph of \(f(x)=x^2\) into the graph of \(g(x)=-6(x-2)^2+5\).