CALCULUS 1 – Algebra review Intervals and Interval Notation.
Algebra 2 1.7 – “Function” Notation · 2009. 9. 22. · 9/22/09 1 Algebra 2 1.7 –...
Transcript of Algebra 2 1.7 – “Function” Notation · 2009. 9. 22. · 9/22/09 1 Algebra 2 1.7 –...
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Algebra 2 1.7 – “Function” Notation
Not going to spend a lot of time on this because it’s SO SIMILAR to stuff you’re already familiar with.
Mainly introducing some new vocab related to “Function Notation”
Old vocab Recent Vocab New Vocab
X-value Input (Domain) Independent Variable
Y-value Output (Range) Dependent Variable
Here’s a question you’re�familiar with:
“Evaluate y = 2x – 5, when x = 4, 6, 8 and 10.”
Input Formula Output
X 2x – 5 y
4 2(4) – 5 3
6 2(6) – 5 7
8 2(8) – 5 11
10 2(10) – 5 15
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Here’s the same question in “Function Notation”:
“Evaluate f(x) = 2x – 5, when x = 4, 6, 8 and 10.”
Indep. Var. Function f(x)
X 2x – 5 y
4 2(4) – 5 3
6 2(6) – 5 7
8 2(8) – 5 11
10 2(10) – 5 15
The character f(x) is read as �“The function of x…”
A FUNCTION is an algebraic expression (ex. 7 – 2x ) that shows how an input value (x) is manipulated mathematically to arrive at its unique output value
Ex. “If f(x) = 7 – 2x, evaluate f(0), f(1/2) and f(-2)”
Solution: Input (x) Function (7 - 2x) Output f(x)
0 7 – 2(0) 7
1/2 7 – 2(1/2) 6
-2 7 – 2(-2) 11
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Examples: If f(x) = 3x2 – x + 2, evaluate f(0), f(1.5), f(-4)
If this is a graph of f(x), evaluate f(-4), f(-1), f(0) and f(4)
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Graph the function g(x) = -2x + 4
p.55 #22 Scuba Diving “In order to scuba dive safely, divers must be aware that
water pressure is a function of depth. The water pressure increases by 0.445 pounds per square inch (psi) for each foot of depth. The pressure at the surface is 14.7 psi.”
1. Write a function to represent Water Pressure.
2. What is the value of the function for an input of 50?
3. What does that represent?
4. Prepare a function table of psi to a depth of 100 feet in 10’ increments.
5. Graph your results.
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1. f(x) = (x – 1)2 + 4 Evaluate for the replacement set {-1, -1/2, 0, 1, 3}
2. Graph the function of the replacement set
3. How do we know by looking at it that this IS a “function”?