Function Notation
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Function Notation Intro
 y = 2x – 2 or y = 5x – 3
 For function notation, we use “f(x)” in place of
“y”
 For functions, the two notations mean the exact
same thing, but "f(x)" gives you more flexibility
and more information.
 The expression "f(x)" means "plug a value for x into a
formula f
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Why do we need this…?
 In textbooks and when writing
things out, we use names like f(x),
g(x), h(x), s(t), etc.
 With this notation, you can now use
more than one function at a time
without confusing yourself or mixing
up the formulas.
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Function Notation
 You used to say "y = 2x + 3; solve for y when x =
–1".
 Now you say "f(x) = 2x + 3; find f(–1).”
 You do exactly the same thing in either case: you
plug in –1 for x and then solve.
 f(-1) = 2(-1) + 3
= -2 + 3
=1
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So…
y = 2x +1
means the same thing as
f(x) = 2x + 1
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Solving the linear equation
f(x) = g(x)
Given: f(x) = 2x – 3
g(x) = 5x + 7
Find the solution for f(x) = g(x).
To solve this problem, all we have to do is set the
two functions equal to each other and then solve
for x.
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2x – 3 = 5x + 7
2x – 3 = 5x + 7
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What is the solution for x in the equation f(x) = g(x), where
F(x) = -5x + 4 + x and g(x) = 4x – 16
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What is the solution for x in the equation f(x) = g(x), where
F(x) = 4(x – 2) and g(x) = 4(2x – 3)
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What is the solution for x in the equation f(x) = g(x), where
f(x) = 24x – 48 and g(x) = 5x – 10
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What is the solution for x in the equation f(x) = g(x), where
f(x) = 5 + 25x and g(x) = -20x + 95
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What is the solution for x in the equation f(x) = g(x), where
f(x) = 32 – 3x and g(x) = 6x – 49
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What is the solution for x in the equation f(x) = g(x), where
f(x) = 5 and g(x) = 5x
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What is the solution for x in the equation f(x) = g(x), where
f(x) = 18x + 24 – 16x + 8 and g(x) = -2x + 16
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What is the solution for x in the equation f(x) = g(x), where
F(x) = 2.5x – 4.8 and g(x) = -1.5x + 91.2
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What is the solution for x in the equation f(x) = g(x), where
F(x) = 2x + 6 and g(x) = 4x – 12
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3
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What is the solution for x in the equation f(x) = g(x),
where
F(x) = x + 2 and g(x) = x – 3
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