From question 1-8 please don't use lim. these questions are from unit 1 which is rational, reciprocal and inequalities.

1. a) Describe the transformations on the cubic function below.

Explain your thinking process.

f(x)=7[21?(x?5)]3?45

b) The point (-9, -2446) is on the transformed function

f(x)=7[21?(x?5)]3?45use the transformation statement the find the original point on the parent function. Justify your answer.

2. Use the characteristics of the given function to graph the function and it's reciprocal on the same set of axes, either using online graphing technology or by hand. State the intercepts and identify any maximum or minimum points, where possible. Explain your thinking process.

f(x)=?x2+7x?6

3. a. Fill in the table_and sketch the graph of the following equation.

f(x)=3x+18?2x?5?

Vertical asymptotes	Horizontal asymptotes	x? intercept	y? intercept	Domain

b. State positive and negative intervals forf(x)=3x+18?2x?5?

Positive interval:

Negative intervals:

4. Find the _real roots of the following rational equations.

a.9x+11?7x??12=x1?

b.x+2x?1?=5x?13x+8?

5. Solve the following inequality algebraically. Explain your process.

8x?3 ? 2x+1 ? 17x-8

6. Solve the following inequality algebraically. Include an interval chart in your solution.

x?115x+4?x+135x?7?

7. The dimensions of a box are 3 cm 5 cm 7 cm. The width, length, and height of the box must be increased by the same amount x in order for the box to have a volume of 693 cm cubed. Determine the value of x that will produce a box with a volume of 693 cm³

8. The specifications for a storage container state that the length is 1 metre more than triple the width and the height is 5 metres less than double the width. Find the range of possible dimensions for a volume of at least 8436 m³ using the algebraic method.

9. Given that f(x) = { (1,3), ( 5,7), (9, 11), ( 13, -5)} and

g(x) = { (-2,33), ( 1,-1), (5, 9)}. Determine the following:

f(x) + g(x) =

g(x) ? f(x) =

f(x) ? g(x) =

10. Given that f(x) = 2x?3 and g(x) = 9x2?5x+11,

determine the following:

a. g(x) ? f(x) =

b. f(x) ? g(x) =

c.g(x)f(x)? = d. g ? f(x) =

11. Use the given graphs to sketch the graph of f(x) + g(x). Explain your process.

f(x)	g(x)	f(x)+g(x)

f(x) 30 20 10g(x) 30 20 10 10\f