1 Ii tie table one of y or z is a function of z and one is n

1. Ii tie table one of y or z is a function of z and one is not. Identify which is not a function and explain why itis is not. Identify 35 40 45 2. For the graph below, identify all turning points and points of inflection; determine all intervals in which the function is increasing, decreasing, concave up and concave down. 0 5 10 15 20 25 30 35 40 45 50 3. For each of the functions below find f(3) (b) f(z)= 4.5-r+1 Find the domain of each of the functions below 4. 2 (b) H(z)= (c) 9(z) =(z+1)-½ Write an equation of the line that 5. (a) Passes through (-6,5) with slope 11. (b) Passes through (15,75) and (-40, 100). 6. A company buys a machine for $600,000, with an expected useful life of 15 years. At the end of the 15 years it will be sold for parts for $30,000. Assuming straight line depreciation (a) Write the equation of the value of the machine as a function of time. (b) Compute the value of the machine at the end of 4 years. (c) Sketch a graph of the equation from part (a). inequalty 2+3) 7. Solve the inequality 8. Use synthetic division and the Rational Roots Test to factor32+2. 9. Sketch the graph of f(z)- 1)(z-3) 2 0. 5

Solution

Ans: 1. z is a function whereas y is not because y has two different values for same x = 10.

2. Turning points: 10, 25, 40 where 10 and 40 are maxima and 25 is minima.

Points of inflection = 20, 30.

Increasing in [0,10] & [25,40] & decreasing in [10, 25] & [40 ,50].

Concave down : [0, 20] & [30 ,50] & Concave up : [20 ,30].

3. a) f (3) = ((3^2)+7) )^1/2 = 16 ^(1/2) = +-4

b is not visible.

4 a) The part under the radical sign should always be greater than or equal to zero. So ,

3x + 2 = 0 3x = -2 x = -2/3. Hence x should be greater than or equal to zero.

4b) The denominator could not be zero. Here denominator is 3x - 1 which is equal to zero at x = 1/3.

So the domain will be all real values of x except 1/3

4c) Like in the part above here x+1 is in denominator so the domain will be all real values of x except where x+1 = 0 which is at x = -1.

5a ) Line equation is of the form y = ax + b where a is the slope of line which is given here to be 11. So the equation chanhes to y = 11x + b. Now line passes through ( -6, 5) & putting these values for x & y in equation we get;

5 = 11*(-6) + b 5 = -66 + b b = 71.

Therefore the equation of line is y = 11x + 71.

5b) here 2 points are given through which the line passes they are (15, 75) & (-40, 100).

Writing the equation y = ax + b & putting the points in it we have 2 equations.

75 = a*(15) + b & 100 = a*(-40) + 100. Subtracting them with each other and solving for a we get a = -5/11 and putting it in any of the equation gives the value of b = (900/11). So the equation becomes

y = (-5/11)a + (900/11) ; simplyfinh further it becomes

y = -5a + 900

That\'s all for this question.