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Calc 8/23

Quiz Review

QuestionAnswer
What is the DOMAIN of a function? The set of all input values. The X values.
What is the RANGE of a function? The set of all output values. The Y values.
How many values of X are there for each value of Y in a standard function? THERE CAN BE ONLY ONE!
How do you determine if a graph of data is a function? If it passes the VERTICAL LINE TEST.
How many values of Y are there for each value of X in an INVERSE function? THERE CAN BE ONLY ONE!
Define the characteristics of an increasing function. As X increases, Y increases. "Slopes" are positive.
Define the characteristics of a decreasing function. As X increases, Y decreases. "Slopes" are negative.
How many radians are in 180º? There are pi radians in 180º.
Define 1 radian. 1 radian is the measurement of the angle, theta, in the sector of a circle when radius length is equal to arc length.
What is the formula for arc length of a sector? Arc length is equal to the radius times theta. L=rΘ
List the 5 types of functions. Trigonometric, exponential, logarithmic, polynomic, rational.
List the six trigonometric functions and what their purpose is. The trigonometric functions sin, cos, tan, cot, sec, and csc are used to measure angles and area.
What is the format of an exponential function? e^x or a^x
What is the format of a logarithmic function? logX in base a or lnX
What is the format of each term in a polynomial? aX^n Where a is any real number, X is a variable, and n is 0 or any positive integer.
Define a rational function. A ratio of two polynomials. Ex: (3x^3+2x^2+x)/(x^2+3x+9)
Define a term. A quantity that is added or subtracted.
Define a factor. A quantity that is multiplied or divided.
Can you cancel terms with factors? One does not simply cancel a term with a factor.
What are the two methods to find the domain of a function? Eliminate X values that create a 0 denominator. Eliminate sections of the real number spectrum which create a negative quantity under a radical with an even root.
If a function is even, how is it symmetric? With respect to the Y-axis.
If a function is odd, how is it symmetric? With respect to the origin.
How do you tell if a function is even? Negate X and simplify. You should get the original function.
How do you tell if a function is odd? Negate X and simplify. You should get the opposite of the original function.
If f(X) is periodic, what happens when you add the period to X? You get f(X).
What should you exclude in the domain of a combined function? Ex: f+g(X) X values of each individual function and additional X values in the combined form.
What are the rules for the domain of a composite function? Ex: f(g(X)) The domain of the composite must include the domain of its inner function. The domain of the composite can NEVER be greater than that of the inner function.
Created by: 100004125431883
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