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Day 6 examples
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This document provides examples of graphing composite functions. It explains that to find the domain of a composite function f(g(x)), you must consider the restrictions on the domains of both the inner and outer functions. It then gives three examples of determining the composite functions f(g(x)) and g(f(x)) for various functions f and g, and calculating or graphing their domains and ranges. The final example asks to determine possible functions f and g that satisfy three given composite functions.
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A polynomial function contains terms of variables raised to whole number powers that are added or subtracted. Examples of polynomials are x^2 + 5x + 3 and 3x^4 - 2x^3 + x^2 - 4. Long division can be used to divide polynomials, with the process being similar to dividing numbers. The result of polynomial division is the quotient polynomial and a remainder.
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Day 8 examples u7w14
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Day 3 examples u7w14jchartiersjsd
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Day 2 examples u7w14jchartiersjsd
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Factorial notation represents the product of all positive integers less than or equal to the given number. For example, 5! = 5 x 4 x 3 x 2 x 1 and 8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1. The document also provides examples of simplifying factorials without a calculator by using properties such as 5! + 4! = 6 x 4! and (k + 1)! + k! = (k + 2)k!.Day 1 examples u7w14
Day 1 examples u7w14jchartiersjsd
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Day 7 examples u6w14
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Day 5 examples u6w14jchartiersjsd
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1. The document discusses composite functions, which involve combining two functions f(x) and g(x) where the output of one is used as the input of the other. It provides examples of evaluating composite functions using tables and graphs.
2. Key steps for evaluating composite functions are: 1) Substitute the inner function into the outer function and 2) Simplify the expression. Order matters as f(g(x)) and g(f(x)) may have different values.
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Day 4 examples u6w14jchartiersjsd
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Day 3 examples u6w14jchartiersjsd
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The document outlines a mental math test covering polynomials. It includes short answer questions testing long division, synthetic division, the remainder theorem, and finding the degree, leading coefficient, and y-intercept of polynomials. The test also covers matching graphs to polynomial equations and word problems involving fully factoring polynomials and two graphs. Multiple choice questions will require explaining solutions, while long answer questions involve fully factoring polynomials and word problems.Day 8 examples u5w14
Day 8 examples u5w14jchartiersjsd
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The document contains two polynomial word problems. The first asks to write a function V(x) to express the volume of a box with dimensions x, x+2, x+10 in terms of x, and find possible x values if the volume is 96 cm^3. The second problem describes a block of ice that is initially 3 ft by 4 ft by 5 ft, and asks to write a function to model reducing each dimension by the same amount to reach a volume of 24 ft^3, and determine how much to remove from each dimension.Day 7 examples u5w14
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The document provides 3 polynomial word problems: 1) finding the equation for a polynomial given its graph f(x) = -(x - 2)2(x + 1), 2) determining the polynomial P(x) when divided by (x - 3) with a quotient of 2x^2 + x - 6 and remainder of 4, and 3) finding the value of a if (x - 2) is a factor of ax^3 + 4x^2 + x - 2. It also gives a 4th problem of determining the value of k when 2x^3 + kx^2 - 3x + 2 is divided by x - 2 with a remainder of 4.Day 5 examples u5w14
Day 5 examples u5w14jchartiersjsd
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Day 3 examples u5w14jchartiersjsd
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This document asks which of the following binomials are factors of the expression 9x - 12. The options given are x + 3 and x - 2. Of these two options, x - 2 is a factor of 9x - 12, since (3x - 4)(3x - 4) = 9x^2 - 12x + 12 = 9x - 12.Day 2 examples u6w14
- 1. Combining Functions by Graphing
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