SOLUTION: I'm a bit confused with these problems. I get it somewhat, but for some reason I get lost after the first few variables. Evaluate function for the value specified. f(x)=x2-7x+

Algebra ->  Graphs -> SOLUTION: I'm a bit confused with these problems. I get it somewhat, but for some reason I get lost after the first few variables. Evaluate function for the value specified. f(x)=x2-7x+      Log On


   

Question 83140: I'm a bit confused with these problems. I get it somewhat, but for some reason I get lost after the first few variables.
Evaluate function for the value specified.
f(x)=x2-7x+10; find (a)f(0), (b)f(5), and (c)f(-2)
Rewrite equation as a function of x
-3x+4y= 11 ( what i don't understand is how i find out how to rewrite this equation.)
this has to be graphed- f(x)=-2x-5 ( does this get graphed like any other equation, i noticed the function notation and got a little confused)
If f(x) =4x-3 then what does this equate to?
f(-1)
Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
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Evaluate function for the value specified.
.
f%28x%29=x%5E2-7x%2B10 find
.
(a) f(0)
.
Just substitute 0 for every x in the equation and reduce as necessary
.
f%280%29=0%5E2-7%2A0%2B10+=+0+-+0+%2B10+=+%2B10
(b) f(5)
.
Substitute 5 for every x in the equation:
.
f%285%29=5%5E2-%287%2A5%29%2B10+=+25+-+35+%2B+10+=+0
.
(c) f(-2)
.
Substitute -2 for every x in the equation:
.
f%28-2%29=%28-2%29%5E2-%287%2A%28-2%29%29%2B10+=+4+-%28-14%29%2B10+=+4+%2B+14+%2B+10+=+28
.
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Rewrite equation as a function of x
-3x%2B4y=+11
.
This problem is just asking you to solve for y. Then replace the y by "f(x)". First, solve
for y. Start by getting the term containing y on one side and everything else on the
other side. So get rid of the -3x on the left side by adding +3x to both sides. This
makes the equation become:
.
4y+=+3x+%2B+11
.
Then solve for y by dividing all terms on both sides of this equation by 4 (which is
the multiplier of y) to get:
.
y+=+%283%2F4%29x+%2B+11%2F4
.
Now just replace y by f(x) and the answer becomes:
.
f%28x%29+=+%283%2F4%29x+%2B+11%2F4
.
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.
This has to be graphed- f(x)=-2x-5
.
(Does this get graphed like any other equation? I noticed the function notation and got
a little confused)
.
I'm going to assume that the "-" sign after the word "graphed" is not associated with the
function. If it is, just make the appropriate changes. (The changes would involve
having -y on the left side of the equation and then changing it to +y by multiplying
the entire equation ... all terms on both sides ... by -1.)
All you
have to do for this problem is replace f(x) by y. This makes the equation to be graphed:
.
y+=+-2x+-+5
.
Now just proceed as you would with any graphing problem. You can assign values to x and
find the corresponding values of y. Then plot each x,y point for the various values of
x. You are creating the graph of f(x).
.
When you get done the graph should look somewhat like:
.
graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C-2x+-5%29
.
*******************
.
If f%28x%29+=4x-3 then what does this equate to?
.
f(-1)
.
Just as we did above, substitute -1 for every x in the equation and you get:
.
f%28-1%29+=+4%2A%28-1%29-3+=+-4-3+=+-7
.
So f%28-1%29 is equal to -7.
.
*******************************
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Hope this helps a little to clarify things for you regarding functional notation and what
it means.