Question
Which of the following describes the difference between the graph of f and the graph of the output of f multiplied by 2?
- The slope changes by a factor of 2; the y - intercept does not change.
- Both the slope and y - intercept change by a factor of 2.
- The slope does not change; the y - intercept changes by a factor of 2.
- Neither the slope nor y - intercept change.
Hint:
Use Horizontal compression.
The correct answer is: Both the slope and y - intercept change by a factor of 2.
Given That:
Which of the following describes the difference between the graph of f and the graph of the output of f multiplied by 2?
>>>Let us consider the function f and it's respective output function:
y = mx + c
->-> We were asked to find the variation of the function if it is multiplied by a factor of 2. Then,
>>> y' = 2mx + 2c
>>>Therefore, the slope of a function becomes double and also the constant doubles.
>>>>hence, we can say that the both the slope and the constant doubles.
From the question it is clear that 
.
So, both the slope and y - intercept change by a factor of 2.
Related Questions to study
Describe the transformation of the function 
that makes the slope 1 and the y - intercept 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.
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.
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.
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.
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.
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.
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 . 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?
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.
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.
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 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.
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.
.
