College Algebra Final Review
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What is the special factorization of A^3-B^3?
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(A-B)(A^2+AB+B^2)
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What is the special factorization of A^3+B^3?
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A+B)(A^2-AB+B^2)
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When is a relation a function?
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If each member of the domain corresponds to exactly one member of the range
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How can you test whether a graph is demonstrating a function?
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Use the vertical line test
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A horizontal line is represented by
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y=#
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A vertical line is represented by
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x=#
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What is the equation for slope?
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(Y2-Y1/X2-X1)
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What is the point slope form equation?
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Y-Y0=m(X-X0)
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How do you test for an odd function?
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Replace x with -x and see if the resulting equation is completely opposite of the original.
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Odd functions are symmetric with respect to the
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x-axis
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How do you test for an even function?
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Replace x with -x and see if the resulting equation is identical to the original
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What does the basic graph y=x look like?
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diagonal line going up towards right corner
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What does the basic graph y-x^2 look like?
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U
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What does the basic graph y=sqrt(x) look like?
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half parabola on right half of graph moving up towards right
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What does the basic graph y=x^3 look like?
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two parabola halves, left bottom is left half of arch, right upper is right half of a u, more vertical
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What does the basic graph y=cube root of x look like?
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two parabola halves, one on left and one on right, more horizontal
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What does the basic graph y=1/x look like?
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Two flipped curves approaching horizontal and vertical asymptotes
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What does the basic graph abs value (x) look like?
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V
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A vertical reflection flips the graph over which axis?
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The x axis
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A horizontal reflection reflects the graph over which axis?
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The y axis
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What is the equation for a vertical reflection?
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-f(x)
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What is the equation for a horizontal reflection?
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f(-x)
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In the function af(x), the graph will stretch ____ by a factor of __ if ___
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vertically, a, abs value (a)>1
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In the function af(x), the graph will shrink __by a factor of ___if ____
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vertically, a, 0<abs value (a)<1
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In the function f(cx), the graph will stretch ___ by a factor of ___ if ___
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horizontally, 1/c, if 0<abs value (c)<1
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In the function f(cx), the graph will shrink ___ by a factor of ___if ___
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horizontally, 1/c, abs value(c)>1
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How would you find the axis from a quadratic equation?
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x: -b/2a, then plug into quadratic for y
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What will the end behavior of a positive coefficient to the even degree leading an equation look like?
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Up on both ends
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What will the end behavior of a negative coefficient to the even degree leading an equation look like?
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Down on both ends
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What will the end behavior of a positive coefficient to an odd degree look like?
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Down on left up on right
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What will the end behavior of a negative coefficient to an even degree look like?
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Up on left, down on right
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How does one find horizontal asymptote?
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Divide leading coefficients of top and bottom
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How does one find vertical asymptotes?
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Set bottom equal to zero
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How does one find zeros?
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numerator equal to zero
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When will an x-intercept be a bounce?
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if it's to an even degree
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When will an x-intercept be a cross?
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if it's to an odd degree
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How do you find a y-intercept of a rational function?
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replace x values with zero
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What does it mean to be one to one?
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Each x corresponds with only one y and each y corresponds with only one x
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How can we test for one-to-one functions?
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Horizontal and vertical line test
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In exponential graphs, exponential growth occurs when in the function a^x ____
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A>1
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In exponential graphs, exponential decay (lowercase L shape) occurs when in the function a^x___
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0<a<1
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In the exponential graph y=a^x, the points (__,__) and (__,___) are always present
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(0,1) (1,a)
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In exponenetial functions, the horizontal asymptote is always y=0 unless
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vertical shift occurs
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To find the y intercept in an exponeniial function, replace x with
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zero
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In logarithmic graphs, growth occurs (in the shape of the left half of an arch) when in the equation logbasea(x), __
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a>1
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In logarithmic graphs, decay occurs (in the shale of a lowercase L) when in the function logbasea(x)__
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0<a<1
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in logarithmic graphs logbasea(x), what two sets of points are always present?
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(1,0) (a,1)
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What does the change of base formula look like for the equation logbasea(x)?
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lnx/lna
