Question

HELP NEEDED ASAP!


2) In words, communicate all transformations made on the parent function f(x)=2^x to sketch the function: [3]

$g(x)=-5$ · $2^{-\frac{1}{3}(x+1) } +7$



3) Consider the sketch of a sinusoidal function provided. Then answer the following

questions with reference to the function.

a) What is the amplitude? _____________ [1]

b) What is the period? _____________ [1]

c) Determine a sine function modeled by this sketch. ______________________ [3]

***show calculations.

Answer 1

The sequence of transformations from the parent function are

• Compressing the function, horizontally by a scale factor or -1/3,
• Compressing the function, vertically by a scale factor or -5,
• Translating the function left by 1 unit
• Translating the function up by 7 units.

The equation of the sinusoidal function is y = -2sin(x + 1.5) - 3

How to determine the transformation?

The function is given as:

g(x) = -5 * 2^-1/3(x + 1) + 7

The above function is an exponential function.

The parent function of an exponential function is

f(x) = b^x

So, the parent function of g(x) = -5 * 2^-1/3(x + 1) + 7 is

f(x) = 2^x

Start by compressing the function, horizontally by a scale factor or -1/3

g(x) = 2^-1/3(x)

Next, compress the function, vertically by a scale factor or -5

g(x) = -5 * 2^-1/3(x)

Next, translate the function left by 1 unit

g(x) = -5 * 2^-1/3(x + 1)

Next, translate the function up by 7 units

g(x) = -5 * 2^-1/3(x + 1) + 7

Hence, the sequence of transformations from the parent function are

• Compressing the function, horizontally by a scale factor or -1/3,
• Compressing the function, vertically by a scale factor or -5,
• Translating the function left by 1 unit
• Translating the function up by 7 units.

See attachment for the graph of the function

The sinusoidal function

The minimum and the maximum of the function are

Minimum = -1

Maximum = -5

The amplitude (A) is calculated as:

A = 0.5 * (Maximum - Minimum)

So, we have:

A = 0.5 * (-5 + 1)

A = -2

The vertical shift (d) is calculated as:

d = 0.5 * (Maximum + Minimum)

So, we have:

d = 0.5 * (-5 - 1)

d = -3

The period (P) is calculated as:

P = 2π/B

From the graph,

B = 1

So, we have:

P = 2π/1

P = 2π

So, the amplitude is -2 and the period is 2π.

The equation of the sine function

In (b), we have:

A = -2

B = 1

d = -3

A sine function is represented as:

y = A sin(Bx + C) + D

So, we have:

y = -2sin(x + C) - 3

The graph passes through the point (0, -5)

So, we have

-5 = -2sin(0 + C) - 3

Solve for C, we have

C = 1.5

So, we have:

y = -2sin(x + 1.5) - 3

Hence, the equation of the sinusoidal function is y = -2sin(x + 1.5) - 3

Read more about sinusoidal function at

brainly.com/question/10700288

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