Which line fits the data graph below?

A student graph . On the same grid, he/she graphs the function g which is a transformation of f made by subtracting 4 from the input of f. Write the equation of the transformed graph.

Given 

So,

The minimum wage for employees of a company is modeled by the function . The company decided to offer a signing bonus of $50. Write the function of g that models the new wage for employees of a company.

The graph of g describes as a _____________ of the graph of f.

Given  and

So, the graph of the function g is the function f translates k units horizontally.

The graph of  is a _____________ of  when k > 1.

Multiplying the output of a linear function f by k scales its graph vertically.
So, when k > 1 the transformed graph is a vertical stretch.

Find the value of k for each function g.

For a given , the graph of the function g is the function f translates k units vertically.
The function of the graph g is translated 3 units up compared to the graph of f.
So, the value of k = 3.

Which of the following describes the difference between the graph of f and the graph of the output of f multiplied by 2?

From the question it is clear that .
So, both the slope and y - intercept change by a factor of 2.

Describe the transformation of the function  that makes the slope 1 and the y - intercept 2.

The cost of renting a landscaping tractor is a $150 security deposit plus the hourly rate is $30/hour. Write the function f that represents the cost of renting the tractor.

The security deposit is constant  that is 150 dollars and the total cost for the tractor is 30x.
>>>Then, the functional representation of the given data is 150 + 30x.

Describe how the transformation of the graph of  compares with the graph of .

The given function function finally becomes 0.2f(x) which is reduced from the given function.
>>>>It is said to be Horizontal stretch.

Write the equation of the transformed function  when the function is vertically stretch by a scale factor of 6.

The function  becomes 3x + 18 after vertical stretch.

The graph of  is a ______ of 

Adding or subtracting a constant k to an input of the function translates the graph horizontally by k units.

Let . Suppose you multiply 3 to the input of the f to create the new function g. Write the equation that represents g?

By Substituting 3x in place of x gives 3x-2.

Describe how the value of k affect the slope of the graph of compared to graph of .

The slopes of the given functions is 2.
>>>Therefore, the slopes of the both equations are same.

Let . Suppose you subtract 3 from the input of the f to create the new function g. Write the equation that represents g?

Horizontal stretch just change the constant of the function.
Putting x-3 in place of x gives  3x-11.

Let . How does the graph of  compare with the graph of f?

The Horizontal Stretch is the variation of the function that stretches the function by multiplying the independent variables with the inverse of the coefficient of the function.
>>>Therefore, we can say that the given function is Horizontally stretched.