Pre-Calc: Find g(x) whose graph is shift of f(x) by 7 units

[CP123]

First of all: Hello everyone! I am in college pre-calculus and I am having some trouble with it. I am doing functions right now.

Consider the following function: f(x) = x^2 - 3x.

Given the function g(x) whose graph could be obtained by shifting the graph of f(x) by 7 units to the right. I am unsure of how to do this.

Thus far, I have come up with x^2-3x-7, which I was told was wrong.

As well, the point (7,0) is a point on the graph of y=f(x). Consider the function g(x) = -f(x) + 5. There is a point on the graph of g(x) such that x = 7. What is the y-coordinate of this point? I'll be honest guys; I'm lost on this one.

Thank you for any help provided

CP123

 

[stapel]

I'll be honest guys; I'm lost on this one.

To start getting un-lost, it would probably be a good idea to study a lesson or two on this topic of function transformations. Once you've learned the basic terms and techniques, you'll understand how "f(x + 7)" relates to f(x) and the listed shifting. :wink:

Eliz.

 

[Loren]

f(x) = x^2 - 3x

When you graph this, the f(x) is "y" on the graph. When you just add or subtract a number from the right side of the equation you are changing the value of y. Therefore, the curve will move up or down.

 

[CP123]

f(x) = x^2 - 3x

When you graph this, the f(x) is "y" on the graph. When you just add or subtract a number from the right side of the equation you are changing the value of y. Therefore, the curve will move up or down.

Thank you for the information. However, I am looking more for how the function would look after the addition of 7 units. Would it be x^2-3x-7? I was told that was wrong, so I am unsure what to do.

 

[Deleted member 4993]

f(x) = x^2 - 3x

When you graph this, the f(x) is "y" on the graph. When you just add or subtract a number from the right side of the equation you are changing the value of y. Therefore, the curve will move up or down.

Thank you for the information. However, I am looking more for how the function would look after the addition of 7 units.

Addition of 7 units - to what? You can add to 'f(x)' or you can add to 'x' - where do you want to add that 7?
Would it be x^2-3x-7? I was told that was wrong, so I am unsure what to do.

 

[Loren]

My suggestion:

Step 1 - Graph: y = f(x) = x^2 - 3x
Step 2 - Add 7 to right side of f(x) getting y = f(x) = x^2 - 3x + 7. Graph that.
Step 3 - Add 7 to x in f(x) getting y = f(x+7) = (x+7)^2 - 3(x+7). Expand and simplify, then graph that.
Step 4 - Compare the three graphs and make a stab at a conclusion.