MAT College Algebra - Gateway 2: Linear Equations and. Name: Date: B

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1 Mathematics Department MAT 10 - College Algebra - Gateway : Linear Equations and Name: Date: 9919 B This exam covers material from Sections 1.1, 1.7,.1,.3, ,.1, and.. The topics covered are function notation and working with linear equations and functions. Students MAY NOT use a graphing calculator on this exam. Unless otherwise indicated exact answers, i.e. 1 3 or p 7, should be given rather than decimal approximations. A 70% or higher AVERAGE on all gateway exams is required to pass College Algebra with a C or better. You may retake the exam at most once per day. The highest grade on the exam is what will be recorded. Note that by earning an 0% or more ON EACH of the first gateway exams, you will be exempt from the last gateway exam. 1. Find f(3) when f(x) = p +x. (1). Find a formula for the linear function f(x) thatsatisfiesf() = andf(9) = 0. ()

2 3. For the function f(x) shown in the graph below, determine f( 3). (3). Find the y-coordinate for the point (,y)onthegraphoff(x) =x +x 1. () 5. Find f( ) when f(x) = x +x 13. (5). The cost per day to society of an epidemic is C =0x +00y where C is in dollars, x is the number of people infected on a given day and y is the number of people who die on a given day. If 115 people are infected on a given day and 13 people die on agivenday,whatisthecosttosociety? ()

3 7. Find the x and y intercepts for the function f(x) =x +1. Writeyouranswersas points. x-intercept y-intercept. In your school supply business, your revenue (in dollars) from selling x thumb drives is given by the linear function R(x) =x, and your cost of stocking x thumb drives is given by the linear function C(x) =5x Find the value of x where R(x) =C(x). (This is known as where you break-even.) () 9. How many solutions does the equation f(x) = haveinthegraphbelow? (9) Linear Equations and Graphing

4 . Find the slope of the line passing through the points (, 3) and ( 9, 1). () 11. Find the location of the point (x, y) wherethelinesy = 5x +andy = x intersect. (11) 1. Write the equation of the line in slope-intercept form (y = mx + b) withslope 7 which passes through the point ( 1, 1). (1)

5 13. Graph y = 5 x Solve the following equation h +7 h = 3. (1) 15. Find the x and y intercepts for the line x +y =. Writeyouranswersaspoints. x-intercept y-intercept

6 Mathematics Department MAT 10 - College Algebra - Gateway : Linear Equations and Name: ANSWER KEY Date: 9919 B f(x) =x $ x-intercept: (. x =1 1, 0) y-intercept: (0, 1) x-intercept: (, 0) y-intercept: (0, 1) 9. Linear Equations and Graphing (, ) 1. y = 7x

7 Mathematics Department MAT 10 - College Algebra - Gateway : Linear Equations and Name: Date: 9919 C This exam covers material from Sections 1.1, 1.7,.1,.3, ,.1, and.. The topics covered are function notation and working with linear equations and functions. Students MAY NOT use a graphing calculator on this exam. Unless otherwise indicated exact answers, i.e. 1 3 or p 7, should be given rather than decimal approximations. A 70% or higher AVERAGE on all gateway exams is required to pass College Algebra with a C or better. You may retake the exam at most once per day. The highest grade on the exam is what will be recorded. Note that by earning an 0% or more ON EACH of the first gateway exams, you will be exempt from the last gateway exam. 1. Find f( ) when f(x) = x. (1). The cost C (in dollars) for renting a car is a function of d and m where d is the number of days the car is rented for and m is the number of miles that the car is driven given by the formula C =30d +0.05m. Determine the total cost of renting a car for 11 days and driving 7 miles. ()

8 3. Find the x and y intercepts for the function f(x) =3x. Write your answers as points. x-intercept y-intercept. For the function f(x) shown in the graph below, determine f(). ()

9 5. How many solutions does the equation f(x) = 9haveinthegraphbelow? (5). Find f( ) when f(x) = x + x +1. () 7. Find the y-coordinate for the point (0,y)onthegraphoff(x) =13x. (7). Find a formula for the linear function f(x) thatsatisfiesf( ) = 1 and f( 9) =. ()

10 9. In your school supply business, your revenue (in dollars) from selling x thumb drives is given by the linear function R(x) =x, and your cost of stocking x thumb drives is given by the linear function C(x) =x +. Find the value of x where R(x) =C(x). (This is known as where you break-even.) (9) Linear Equations and Graphing. Find the location of the point (x, y) wherethelinesy =7x 5andy =x intersect. () 11. Solve the following equation 5x +30=5x. (11) 1. Find the slope of the line 7x +y = 11. (1)

11 13. Write the equation of the line in slope-intercept form (y = mx + b) withslope 1 which passes through the point (, 5). (13) 1. Find the x and y intercepts for the line 3x +y =. Writeyouranswersaspoints. x-intercept y-intercept 15. Graph y = 1 5 x.

12 Mathematics Department MAT 10 - College Algebra - Gateway : Linear Equations and Name: ANSWER KEY Date: 9919 C 1.. $ x-intercept: (, 0) y-intercept: (0, ) f(x) = 1x x =3 Linear Equations and Graphing. (5, 30) y = x x-intercept: (, 0) y-intercept: (0, 1)