Question

# Let . Suppose you subtract 5 from the input of the f to create the new function g, then multiply the input of the function g by 3 to create a function h. Write the equation that represents h?

Hint:

### We have given f(x) and we have to find g(x) and h(x) given that g(x)= f(x-5) and h(x)=g(3x).

## The correct answer is:

### Given function

Subtract 5 from the input of the

Multiply the input of function by 3

So,.

### Related Questions to study

### If is the transformation of after a vertical compression by , a shift right by 2, and a shift down by 4. What a function for .

>>>Vertical shift of f(x) by 3/4 becomes 3/4(x)

>>>Shifting right the function becomes 3/4(x-2)

>>>Shifting right the function gives 3/4(x-2)-4.

### If is the transformation of after a vertical compression by , a shift right by 2, and a shift down by 4. What a function for .

>>>Vertical shift of f(x) by 3/4 becomes 3/4(x)

>>>Shifting right the function becomes 3/4(x-2)

>>>Shifting right the function gives 3/4(x-2)-4.

### Which of the following describes the difference between the graph of f and the graph of the input of f multiplied by 5?

From the question it is clear that .

So, the slope changes by a factor of 5; the y - intercept does not change.

### Which of the following describes the difference between the graph of f and the graph of the input of f multiplied by 5?

From the question it is clear that .

So, the slope changes by a factor of 5; the y - intercept does not change.

### A student graph . On the same grid, he/she graphs the function g which is a transformation of f made by multiplying to the output of f. Write the equation of the transformed graph.

Given

So,

### A student graph . On the same grid, he/she graphs the function g which is a transformation of f made by multiplying to the output of f. Write the equation of the transformed graph.

Given

So,

### Which line fits the data graph below?

### 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,

### 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 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 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.

### 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.

### 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.

### 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.

### 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.