Math 30 – Worksheet on Linear Equations and Graphs Name: Problem 1: (a) Plot the points  0,2 and  2,5 . Also sketch the line L determined by these points. (b) Use the graph of L to find its slope....

I have 5 worksheets, 2 questions per worksheet. All I need is the steps how you got the answer and the answer itself. The topic Is mostly functions, should be simple to do.


Math 30 – Worksheet on Linear Equations and Graphs Name: Problem 1: (a) Plot the points  0,2 and  2,5 . Also sketch the line L determined by these points. (b) Use the graph of L to find its slope. (c) Use the formula for slope to find the slope of L, twice. (Switch the order in which you plug in the points.) (d) State the y – intercept of L. (e) State the equation of L in slope-intercept form: y mx b  (f) Verify that the point  2,5 is a solution of the equation you stated in part (e). (g) Use the graph of L to find another point on L and verify that it is a solution of the equation you stated in part (e). Problem 2: (a) Plot the points  3, 1 and  3,3 . Also sketch the line L determined by these points. (b) Use the graph of L to find its slope. (c) Use the formula for slope to find the slope of L, twice. (Switch the order in which you plug in the points.) (d) State the y – intercept of L. (e) State the equation of L in slope-intercept form: y mx b  (f) Verify that the point  3,3 is a solution of the equation you stated in part (e). (g) Use the graph of L to find another point on L and verify that it is a solution of the equation you stated in part (e). Use the graph of the function f given here to answer the following questions Math 30 – Worksheet on Functions Name: Problem 1: Use the graph of the function f given here to answer the following questions. (a) Find  2f  . (b) Find  3f . (c) Solve for x:   1f x   (d) Solve for x:   4f x  (e) State the domain of f. (f) State the range of f. Problem 2: Each table below gives several ordered pairs (or points) which satisfy some function. Without plotting points, determine whether or not each function is (or could be) linear. If the function appears to be linear, then find the slope-intercept equation of the graph of the function. 1. 2. ( ) 0 4 1 0 2 4 3 8 x f x   ( ) 1 11 2 6 3 1 4 4 x g x    3. 4. ( ) 0 7 1 5 3 1 4 1 x f x    ( ) 1 3 1 6 3 15 5 24 x h x   5. ( ) 3 0 5 4 6 8 7 12 x p x Key for Problem 2 1. The function appears to be linear. ( ) 4 4f x x   2. The function is not linear. 3. The function is linear. ( ) 2 7f x x  4. The function is linear. 9 3 ( ) 2 2 h x x  5. The function is not linear. Intermediate Algebra Math 30 – Worksheet # 3 Functions Name: 1. Let   1 4 2 x f x x    . (a) Find  0f . (b) Find  1f  and simplify. (c) Find  3f  and simplify. (d) Find  f b . (e) Find  1f x  and simplify. (f) Find the domain of f. State your answer using set notation. 2. The graph below determines a function f. -1 0 1 (c) Find  2f  . (d) Find  0f . (e) Solve for x:   1f x   (f) Solve for x:   3f x  (g) Find any numbers x such that ( )f x x . If there are any such numbers, indicate how to find them. Intermediate Algebra Math 30 – Worksheet # 4 on Linear Models Name: 1. In 2000 the life expectancy of males born in that year was 74.3 years. In 2010 it was 76.2. Let  E t represent the life expectancy of a male who is born t years since 2000. (a) State the two data points  , ( )t E t . (b) Assuming that the change in life expectancy is linear, find a formula for  E t . (c) Use the function found in part (b) to predict the life expectancy of a male born in 2020. State your answer in a complete sentence. 2. Suppose that coffee suppliers can sell 7.0 million lb of coffee at $12 per pound and can sell 5.0 million lb at $15 per pound. Let p be the price per pound and let  A p be the amount sold (in millions of pounds). (a) State the two data points  , ( )p A p . (b) Assuming that the change is linear, find a formula for ( )A p . (c) Use the function found in part (b) to predict the amount of coffee that suppliers could sell at $6 per pound. State your answer in a complete sentence. Math 30 – Worksheet # 5 on Section 9.1 Name: Problem 1: Let   2f x x x  and   1g x x  (a) Find   (4)f g (b) Find   (4)g f (c) Find   ( )f g x and simplify if possible. (d) Find   ( )g f x and simplify if possible. (e) Find   ( )f f x . Do not simplify. Problem 2: Let   3 6 2 x f x   . (a) Sketch the graph of f. (b) Does f pass the horizontal line test? Does f have an inverse function? (c) Find the inverse of f. Write your final answer using inverse function notation. (d) On the coordinate system above, sketch the graph of 1f  . Also sketch the graph of y x with a dashed line.