Expert answer:Understand Function

  

Solved by verified expert:Complete the following problems. Be sure to show all work. Evaluate each function at the given values and simplify.Determine whether the following sets of ordered pairs represent a function.Find and simplify the difference quotient.Use the vertical line test to determine if y is a function of x.Determine the domain and range of the function. Write the answer in interval notation.Find the slope of the line passing through the given points.Given the slope and a point, find the equation of the line. Write your final answer in slope-intercept form.Find the slope, x-intercept, and y-intercept of the following linear functions. Use the information to sketch the corresponding graph. ; find , , and find ; , and ; find , , and (2, 4) and (–1, 10) (3, 5) and (–1, 0) m = 2, (–3, 4) m = ,(1, 7) m is undefined, (2, 3) y = 4x – 5 4x + 2y = 6 3x – 2y + 11 = 0
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College Algebra
Assignment Handouts
Assignment 4.1: Understanding Functions
Complete the following problems. Be sure to show all work.
1) Evaluate each function at the given values and simplify.
a.
f ( x)  x 2  3x  4 ; find f (6) , f (2) , and f ( x  1)
b.
f ( x) 
c.
x3
find f (1) ; f (3) , and f ( x  2)
x
 x2 x0
; find f (4) , f (0) , and f ( 2)
f ( x)   2
x  3 x  0
2) Determine whether the following sets of ordered pairs represent a function.
a. {(1,5), (1, 6), (0,1), (2, 4)}
b. {(0, 2), (1, 6), (2, 4), (5, 2)}
c. {(1, 4), (5, 6), (5,1), (7,1)}
3) Find and simplify the difference quotient.
a. f ( x)  3 x  7
b.
f ( x)  x 2  2 x  8
4) Use the vertical line test to determine if y is a function of x.
a.
b.
College Algebra Handout Assignment 4.1, V2.4
© 2012 Pearson Education
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2/11/2018
College Algebra
Assignment Handouts
c.
5) Determine the domain and range of the function. Write the answer in interval
notation.
a.
b.
College Algebra Handout Assignment 4.1, V2.4
© 2012 Pearson Education
Page 2 of 3
2/11/2018
College Algebra
Assignment Handouts
c.
6) Find the slope of the line passing through the given points.
a. (2, 4) and (–1, 10)
b. (3, 5) and (–1, 0)
7) Given the slope and a point, find the equation of the line. Write your final
answer in slope-intercept form.
a. m = 2, (–3, 4)
b. m = 
3
,(1, 7)
4
c. m is undefined, (2, 3)
8) Find the slope, x-intercept, and y-intercept of the following linear functions.
Use the information to sketch the corresponding graph.
a. y = 4x – 5
b. 4x + 2y = 6
c. 3x – 2y + 11 = 0
College Algebra Handout Assignment 4.1, V2.4
© 2012 Pearson Education
Page 3 of 3
2/11/2018
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