Discuss the below problem:
Q1. Find a linear function perpendicular to the function y= -5x + 12 at the point (2,5) in standard form, point slope form, and slope-intercept form.
Q2. A ball is thrown up into the air.Measurements are taken and a function is found to model the height of the ball versus the time the ball is in the air. The function derived from the data, H(t) = -4.92 + 40.5t + 25.3, is the model for the height of the ball, H(t) in meters, at time t (in seconds)
a) Calculate H(1.672) and interpret the meaning of this result?
b) Find the domain & range of the function H(t)
Q3. A business has a product that is sold in many local outlets. This product sells for $39.95 each. The weekly fixed cost of the business is $2675/week and each additional unit sold costs the company $17.85 to produce and sell.
a. How much revenue is generated on the sale of 349 units? What is the cost of selling units?
b. Create models for the revenue and the cost of sales for the sales of this product.
c. Remembering that profit is revenue minus cost of sales, create a profit model from the revenue and the cost of sales models.
d. Find the number of units you need to sell to "breakeven".
e. What is the inverse of the profit function? Use this function to determine the number of units needed to be sold so that the profit is $13,000.
Q4. The height of a football (as a function of the horizontal distance traveled) is given by the function h(x) = 0.75x - 0.0192x2, where all measurements are in meters. Rewrite the function in vertes form and use the information to determine the initial horizontal and vertical position of the football.
Q5. Find a linear equation (in slope-intercept, point-slope and standard forms) for the line through the points (2,4) and (-1,5)
Q6. Find the inverse of the following functions:
a) f(x) = -5x + 7
b) g(t) = 3√t+6
Q7. Find the following functions f(x) = -6x+5 and g(x) = 3x2 - 10 simplify results
a) (fg)(x) =(-6x+5)(3x2-10) = (-6x + -50)3x2
b) (g+f)(x) = 3x2-10+ -6x+5=-5+6x+3x2
c) 3•g(x-4) = 3(3x2-10)-4 = 3x2-30-4 = 3x2-26