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

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. 

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

Horizontal translation is the function variation that relates the properties of a function and shifts a function to horizontally to obtain the other function.

The graph of  is a _________ of  when 0 < k < 1.

Multiplying the output of a linear function f by k scales its graph vertically.
So, when 0 < k < 1 the transformed graph is a vertical compression.

Describe how the function  compares with the graph of the function 

f(x) = 5x+3 and g(x) = 5(x-2)+3
>>>Then, By comparing the terms of equations there is exactly 2 units shift of g(x) to right to reach f(x).

Describe how the graph of the function  compares with the graph of the function 

Vertical stretch is a type of compression of the functions with the independent variable.

The two points on the graph are given by the function .

Identify the two points on the graph.

The pollution level in the centre of a city at 6 am is 30 ppm (parts per million) and it grows in a linear fashion by 25 ppm (parts per million) every hour. If  y is pollution and t is the time elapsed after 6 am, then determine the function that relates y  with t .

A car rental charge is 100 dollars per day plus 0.30 dollars per miles traveled. Determine the function of the line that represents the daily cost by the number of miles traveled.

For such questions, we should know about the concept of function.

Evaluate the function 

For such questions, we should know the concept of the function.

Identify the function that is linear.

For such questions, we should know the concept of linear functions.

Ramona’s garage charges the following labor rates. All the customers are charged for at least 0.5 hr.

Write the linear function for the data in the table.

A linear function forms a straight line in a graph. It is usually a polynomial function with a degree of 1 or 0, and the equation f(x) = mx + b, where b and m are real numbers. Isn't it similar to the slope-intercept form of a line, which is written as y = mx + b? Yes, because a linear function represents a line.
¶Examples from daily life
1. To print logos on T-shirts, a t-shirt company charges a one-time charge of $50 and $7 per T-shirt. As a result, the total cost is given as a linear function f(x) = 7x + 50, where 'x' is the total number of t-shirts.
2. In linear programming problems, linear functions represent an objective function to minimize costs or maximize profits.
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A copy shop can produce a course reader at a cost of $25 per copy. The monthly fixed costs are $10,000. Determine the total monthly cost as a function of the number of copies produced.

A chemical plant was found to be discharging toxic waste into a waterway. The state in which the chemical plant was located fined the company $125,000 plus $1,000 per day for each day on which the company continued to violate water pollution regulation. Express the total fine as a function of the number of days in which the company remains in non-compliance.

For such questions, we should know the concept of function.