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name: Mathematics 141 fifth homework due Monday, January 27, 2014 show your work to get credit for each problem √ 14. The graph of y = x is vertically stretched by a factor of two, and then is reflected across the x-axis. Write down the equation of this new modified graph. 13. The graph of y = x3 is moved two units to the right and then shifted down five units. Write down the equation of this new modified graph. 15. Find an equation for each graph sketched below: y y half-parabola 2 2 x -2 x -3 y 2 1 x 1 parabola 16. Suppose that a city’s transit ridership x and the price per ride p are linearly related. The transit ridership is two million when the fare is $2 per ride, while the ridership is only 1.75 million when the fare is $2.10. • find the linear relation between x and p • the total revenue from fares R = px. Write R as a function of p. page two 17. A square-bottomed rectangular box with no top is to contain a volume of eight cubic feet. Let x be equal to the length of a side of the square bottom, and let h be equal to the height of the box. Write the surface area A of the box as a function of x. 18. Simplify the difference quotient f (x + h) − f (x) for the function f (x) = 5−3x . h 19. Find a formula for a linear function F whose average rate of change is equal to 4/5 and for which F (10) = 30. 20. Solve the absolute value inequality: |x − 53| < 3.