Function Families

Mrs Lenox Math Help: Function Families

Absolute Value

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Absolute value graph

Domain: all real numbers. Range: UP: (k,∞). The left coordinate will be the y coordinate of the vertex. DOWN: the left value is -∞ and the right coordinate is the y coordinate of the vertex. When you write up increasing and decreasing intervals, use the x coordinate of the vertex. The x interceptsare zeros on the calculator. For y intercept, put 0 in for x in the equation and solve for y.

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Quadratic/Even Degree

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Graph of quadratic

Domain: all real numbers. Range: UP: (k,∞). The left coordinate will be the y coordinate of the vertex. DOWN: (- ∞,k) the right coordinate is the y coordinate of the vertex. End behavior: If the lead coefficient(a) is positive, both sides up. If the lead coefficient is negative,both sides down. Increasing and decreasing intervals, use the x coordinate of the vertex. The x intercepts are zeros on the calculator. For y intercept, put 0 in for x in the equation and solve for y.

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Cubic/Odd Degree

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Graph of cubic

Domain: all real numbers. Range: All real numbers. End Behavior: If the lead coefficient is positive,the end behavior is left side down, right side up. If the lead coefficient is negative, left side up, right side down. When you write up increasing and decreasing intervals, use the x coordinate of the turning point. The x intercepts are zeros on the calculator. For y intercept, put 0 in for x in the equation and solve for y.

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Rationals

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Graph of rational

Domain: all real numbers,x ≠ 0 (exclude numbers that turn denominator into zero). End Behavior:If the degree of the bottom is bigger, horizontal asymptote y=0.If the degree of the top is bigger, no horizontal asymptote. If the degree of the two is the same, the horizontal asymptote is y= ratio of the lead coefficients. Vertical asymptotes : the x values that make the denominator turn into zero after the equation is simplified. For the x intercepts set the numerator equal to zero, and solve for x. For y intercept, put 0 in for x in the equation and solve for y.

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Exponential

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Graph of exponential

Domain: all real numbers. Range:All positive numbers. HA y=0. The x intercepts are zeros on the calculator.The parent function won't have an x intercept since there is a horizontal asymptote at y=0. For y intercept, put 0 in for x in the equation and solve for y. For the parent function it's 1, since any number raised to the zero power is 1.

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Logarithms

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Graph of logarithm

Logarithms are the inverses of the exponential functions, so domain and range are backwards from those. Domain: All positive numbers (0,∞).Range: All real numbers. Vertical Asymptote:x=0. The x intercepts are zeros on the calculator. For the parent,there's one at 1. For y intercept, put 0 in for x in the equation and solve for y. For the parent there won't be one, since there's a vertical asymptote at x=0.

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Practice Problems

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