Sketch the function by hand -- I'm confused on how to do this

[kvilv113]

Homework Statement

Sketch by hand the function

Relevant Equations

f(x) = 1/28 (7√−16x^2 + 16x + 5 + 12)

Sketch by hand the function determined as f(x) = 1/28 (7√−16x^2 + 16x + 5 + 12) and then From the sketch, determine the domain and range of f in interval notation. Hint: Interpret f as part of a circle. You must include in your solutions the inputs and outputs you used to help you sketch the graph of f.

 

[FactChecker]

Two problems with your post:
1) It's not clear how much is under the square root. Use parentheses to make it clear.
2) For homework-type problems, we are only allowed to give hints and guidance to the correct solution. You have to do the work and show it. You do not show any work.

 

[berkeman]

Homework Statement:: Sketch by hand the function
Relevant Equations:: f(x) = 1/28 (7√−16x^2 + 16x + 5 + 12)

Sketch by hand the function determined as f(x) = 1/28 (7√−16x^2 + 16x + 5 + 12) and then From the sketch, determine the domain and range of f in interval notation. Hint: Interpret f as part of a circle. You must include in your solutions the inputs and outputs you used to help you sketch the graph of f.

Welcome to PF.

Well, first of all please format the equation a little better so we can see what it is. There appear to be missing parenthesis and an abiguous placement of a square root sign.

It's best if you use LaTeX to post math equations. That makes them unambiguous and easier to read. I can try to guess at your equation and post it in LaTeX, but I could easily get it wrong...

 

[berkeman]

Maybe...?
$$f(x) = \frac{1}{28} 7 \sqrt{−16x^2 + 16x + 5 + 12}$$

 

[kvilv113]

Maybe...?
$$f(x) = \frac{1}{28}(7 \sqrt{−16x^2 + 16x + 5 + 12}$$

but the 12 isn't in the root sorry i didnt know how to post the equation better

 

[berkeman]

So more like this maybe?
$$f(x) = \frac{1}{28} 7 \sqrt{−16x^2 + 16x + 5} + 12$$

 

[kvilv113]

yes
exactly

 

[berkeman]

BTW, you can click the "Reply" link in the lower right of my post in order to see how I posted that LaTeX. You may need to click the "[ ]" BB-toggle icon in the upper right of the Edit window to get the raw LaTeX view.

Be sure to look through the "LaTeX Guide" link at the lower left of the Edit window to learn more.

 

[berkeman]

yes
exactly

Okay, so to start sketching it, just make a table of x,f(x) and start plugging in integers for x. I'd start with 0, 1, 2, ... etc, and then go back and plug in some negative numbers for x...

 

[Mark44]

So more like this maybe?
$$f(x) = \frac{1}{28} 7 \sqrt{−16x^2 + 16x + 5} + 12$$

yes
exactly

First thing to do is to simplify 7/28.
Then, what I would do is to figure out the domain. For the square root to produce a real number value, it must be true that $-16x^2 + 16x + 5 \ge 0$. You can do this by completing the square. Presumably you've already studied this technique if the book is asking you to plot a graph of this function.