Question 83140
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Evaluate function for the value specified.
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{{{f(x)=x^2-7x+10}}} find 
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(a) f(0)
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Just substitute 0 for every x in the equation and reduce as necessary
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{{{f(0)=0^2-7*0+10 = 0 - 0 +10 = +10}}}

(b) f(5) 
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Substitute 5 for every x in the equation:
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{{{f(5)=5^2-(7*5)+10 = 25 - 35 + 10 = 0}}}
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(c) f(-2)
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Substitute -2 for every x in the equation:
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{{{f(-2)=(-2)^2-(7*(-2))+10 = 4 -(-14)+10 = 4 + 14 + 10 = 28}}}
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Rewrite equation as a function of x

{{{-3x+4y= 11}}}  
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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:
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{{{4y = 3x + 11}}}
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Then solve for y by dividing all terms on both sides of this equation by 4 (which is 
the multiplier of y) to get:
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{{{y = (3/4)x + 11/4}}}
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Now just replace y by f(x) and the answer becomes:
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{{{f(x) = (3/4)x + 11/4}}}
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This has to be graphed- f(x)=-2x-5 
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(Does this get graphed like any other equation? I noticed the function notation and got 
a little confused)
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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:
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{{{y = -2x - 5}}}
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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).
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When you get done the graph should look somewhat like:
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{{{graph(300,300,-10,10,-10,10,-2x -5)}}}
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If {{{f(x) =4x-3}}} then what does this equate to?
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f(-1)
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Just as we did above, substitute -1 for every x in the equation and you get:
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{{{f(-1) = 4*(-1)-3 = -4-3 = -7}}}
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So {{{f(-1)}}} 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.