sample_midterm-3

# Sample_midterm-3 - (d Graph the function(e Based on the graph ﬁnd the range 5 Find the domain of the given function(a f x = √ x − 2(b f x = 4

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Mathematical Functions Sample Midterm Exam In the following problems you are required to show all your work and provide the necessary explana- tions everywhere to get full credit. 1. Find an equation of the line with the given properties: Perpendicular to the line 6 x 2 y = 5; containing the point (2 , 3) . Graph this line. Find its x- and y-intercepts. 2. Determine algebraically whether the following function is even, odd, or neither. (a) f ( x ) = | x | (b) f ( x ) = x 3 x

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3. Answer the questions about the following function: f ( x ) = x 2 x 2 . (a) Is the point (-1, -4) on the graph of f ? (b) What is the domain of f? (c) List the x-intercept(s), if any, of the graph of f. (d) List the y-intercept(s), if any, of the graph of f.
4. Let f ( x ) = | x | if x < 2 x + 1 if 2 x < 3 1 x if x 3 (a) Find f ( 3) , f ( 2) , f (3) . (b) Find the domain of the function. (c) Locate any intercepts.

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Unformatted text preview: (d) Graph the function. (e) Based on the graph, ﬁnd the range. 5. Find the domain of the given function: (a) f ( x ) = √ x − 2 (b) f ( x ) = 4 1 − x 2 6. Graph the function f ( x ) = 2 − 1 x + 1 using the techniques of shifting and/or reﬂecting. Show all steps!!! 7. Given f ( x ) = 1 x and g ( x ) = x + √ 1 − x, ﬁnd the following expressions: (a) ( f ◦ g )(1) [Evaluate!] (b) ( g ◦ f )(1) [Evaluate!] (c) ( f ◦ f )( x ) (d) ( g ◦ g )( x ) 8. The function f ( x ) = 1 − x 3 is one-to-one. (a) Find the inverse of f. (b) State the domain and range of f. (c) State the domain and range of f-1 . (d) Graph f, f-1 , and y = x on the same coordinate plane. 9. Use transformations to graph the function f ( x ) = √ 1 − x − 2 ....
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## This note was uploaded on 02/27/2012 for the course MATH 8650 taught by Professor Kiryltsishchanka during the Spring '12 term at NYU.

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Sample_midterm-3 - (d Graph the function(e Based on the graph ﬁnd the range 5 Find the domain of the given function(a f x = √ x − 2(b f x = 4

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