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Coordinate Algebra EOCT Review In-Class Work Unit 3: Linear & Exponential Functions 04.21.2015 Key Takeaways: 1 EOCT Prep Know your terminologies: A “relation” is any mapping or relationship between two quantities. A relation has an “input” and and “output”. A “function” is a quantitative relation where each member in the domain is assigned to one and exactly one member in the range. A function can be written (or expressed) algebraically in two general forms: Equation Notation: y = 2x + 1 Function Notation: f(x) = 2x + 1 Domain: The set of all possible input values. Also known as “independent variable”, the “cause”, or the “argument” Range: The set of all possible output values. Also known as “dependent variable”, “the effect”, the “result” An “intercept” is a point at which either the input or the output is equal to zero. The x-intercept (x,0) is when y=0. A function can have more than one x-intercept. A y-intercept (0,y) is when x=0. A function can have at most one y-intercept. A minimum is the lowest possible value for the function. A maximum is the highest possible value for a function. Both the MIN and MAX are referred to as “extrema”. End behaviors of functions are the values of “y” (output) as “x” (input) approaches - or +. Forms of functions we’ve examined: Linear: f(x) or y = mx + b Exponential: f(x) or y = ab x
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Coordinate Algebra EOCT Review In-Class Work
Unit 3: Linear & Exponential Functions04.21.2015
Key Takeaways:
1 EOCT Prep
Know your terminologies:
A “relation” is any mapping or relationship between two quantities. A relation has an “input” and and “output”.
A “function” is a quantitative relation where each member in the domain is assigned to one and exactly one member in the range. A function can be written (or expressed) algebraically in two general forms:
Equation Notation: y = 2x + 1 Function Notation: f(x) = 2x + 1
Domain: The set of all possible input values. Also known as “independent variable”, the “cause”, or the “argument”
Range: The set of all possible output values. Also known as “dependent variable”, “the effect”, the “result”
An “intercept” is a point at which either the input or the output is equal to zero. The x-intercept (x,0) is when y=0. A function can have more than one x-intercept. A y-intercept (0,y) is when x=0. A function can have at most one y-intercept.
A minimum is the lowest possible value for the function. A maximum is the highest possible value for a function. Both the MIN and MAX are referred to as “extrema”. End behaviors of functions are the values of “y” (output) as “x” (input) approaches - or +.
Forms of functions we’ve examined:
Linear: f(x) or y = mx + b Exponential: f(x) or y = abx
Exponential Growth / Decay f(n) or y = A (1r)n
Sequences: f(n) or an = a1 + d(n-1) OR f(n) = an = a1(rn-
1)
Coordinate Algebra EOCT Review In-Class Work
Unit 3: Linear & Exponential Functions04.21.2015
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Coordinate Algebra EOCT Review In-Class Work
Unit 3: Linear & Exponential Functions04.21.2015
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Coordinate Algebra EOCT Review In-Class Work
Unit 3: Linear & Exponential Functions04.21.2015
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Coordinate Algebra EOCT Review In-Class Work
Unit 3: Linear & Exponential Functions04.21.2015
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Coordinate Algebra EOCT Review In-Class Work
Unit 3: Linear & Exponential Functions04.21.2015
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Coordinate Algebra EOCT Review In-Class Work
Unit 3: Linear & Exponential Functions04.21.2015
KEY1. f(7) = 2(7) – 1 = 13
2. Domain: {xW (whole numbers), x 0}
C(2000) = 5000 + 1.3 (2000) = $7600C(X) < 10,000 = 5000 + 1.3 (3846). Note C(3846) = 5000 + 1.3 (3846) = $9,999.80
3. a1 = 5. a3 = 11. an = an-1 + 2n-1 . . . an = 3 + 2n
Range (output) will be the set of values that satisfy an = 3 + 2n for n Natural numbers.
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Domain: {xN}. Range (outputs) will be the set of values that satisfy an = 4n – 1 for n N.
5. B: f(x) = -2x + 7
6. D: Recursive formula: an = 4 an-1 For reference, explicit formula: an = 4n-1
7. From the table, f ( x )= 43x+8.
f(x) g(x)Domain (x) All Real All RealRange (y) All Real All Real
8. C: an = an-1 + 2. (current term = the previous term + 2)
7 EOCT Prep
n 1 2 3 4 5
f (n) = -(1-4n) 3 7 11 15 19
Coordinate Algebra EOCT Review In-Class Work
Unit 3: Linear & Exponential Functions04.21.2015
KEY9. D: f(x) = 3x + 5
10. C: f(x) = 4(x) – 20
11. D: C = 3.14 x d
12. The graph is represented by f(x) = 3 + ½ x. B: Point (-2,2).
13. C: “x” = number of nights, and “y” = total cost for the camp site.
14. C: Because you can have only one output for any give input, replace one of the x = -2 with something other than x = -2.
15. C: f(3) = 33 – 2 = 25
16. D: tripling each year is the same as an = 3 (an-1)
8 EOCT Prep
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