**PRE-TEST FOR MATH REFRESHER ONLINE COURSE **

** 1.** Linear Equations are recognized because:

** 2.** Slope-Intercept Format would be:

** 3.** The slope of a line is defined as:

**4.** Given the equation: 3x + 2y = 10, the slope of the line and y intercept of this equation would be:

** 5.** Given the system of equations, solve this system, if a solution exists:

** x + y – z = 2 **

** 3x + y – z = -2 **

** 4x – 2y + z = -13 **

** 6.** Given the system of equations, solve this system, if a solution exists:

**5x – 4y = 9 **

** x = 2y – 3**

**7**.Given the relation, z, of ordered pairs:

z = {(john, rangers game), (lee, rangers game), (john, stars game)}

** 8. ** The domain of the function, f (x) = 2x -5 is:

** 9.** Given the function, f (x) = -3x/2 + 4, evaluate f (x – a):

** 10. ** The composition of two functions, f (x) and g (x) is defined as:

** 11.** Given: f (x) = 4x – 3, g (x) = 5x^{ 2} – 2; Find: ** f ◦ g **

^{ 2 }– 2

^{ 2} -11

^{2} – 3

** 12. ** The Supply and Demand functions for the production of an electronic toy is:

**
S (x) = x ^{2} + 10x + 20 **

**
D (x) = 28 + 12x **

** **

Find the market equilibrium price point in dollars.

** 13.** If a product is sold for less than the supply = demand price point,

there may be a:

** 14.****Given:** f (x) = 1/x , g (x) = x ; Find: ** f ◦ g **

^{ 2}

** 15. ** If the inverse of a function exists, then the following would be true:

** f ^{-1} **

**◦**

**f = 1**

**f ^{-1} **

**◦**

**f = x**

** f ^{-1} **

**◦**

**g = x**

**f ^{-1} **

**◦**

**g = 1**

** 16. ** If the inverse of a function exists, when the function and its inverse are both drawn on the same graph, the following will occur:

** 17.****Given:** f (x) = x – 3 ; **Find:** f ^{-1}

**
**

** 18.****Given:** f (x) = 2/(x – 3) , g( x) = 2/x + 3

Are these two functions inverses of each other?

** 19.** Evaluate the following limit:

lim _{x –> ∞ }(x^{3} – 2x + 5)/(2x^{3} – 7)

** 20. ** The derivative of the function f, at x, is known as:

** 21.** Given: f (x) = (-1/3)x^{2} + 7x – 2 . The derivative of f with respect to x is:

** 22.** Given: z = f (x, y) = x^{ 2 }+ y^{2} + xy – 5

Find partial derivatives f_{ x} and f_{ y} of the given function.

_{ x }(x, y) = 2y + 2x ; f_{ y} (x, y) = 2x + 2y

_{ x }(x, y) = 2x ; f_{ y} (x, y) = 2y

_{ x } (x, y) = 2x + y ; f_{ y} (x, y) = 2y + x

_{ x } (x, y) = 2 + x ; f_{ y} (x, y) = 2 + y

** **

** 23. ** Given: z = f (x, y) = x^{2} + 3xy – 4y^{2}

** Find** partial derivatives f x and f y of the given function.

_{x }(x, y) = 2x + 3y ; f _{y} (x, y) = 3x – 8y

_{x } (x, y) = 3y + 8y^{2 }; f _{y} (x, y) = 2x + y

_{x } (x, y) = 2y + x ; f _{y} (x, y) = 3x + y

_{x } (x, y) = 2y + x ; f_{ y} (x, y) = 2x + 4y

** 24. ** Given: z = f (x, y) = (3y)/(2x)

Find partial derivatives f _{x} and f _{y }of the given function.

_{x }(x, y) = – 3y/2x ^{2 }; f _{y} (x, y) = 3/2x

_{x} (x, y) = -3y/2x ; f _{y} (x, y) = 2x

_{x} (x, y) = – 3y/2x ; f _{y} (x, y) = 3/x

** 25. ** The “first derivative test” will help determine if a point on the graph of

the function y = f (x) :

** 26. ** **Given the function:** f (x, y) = xy ^{2}

Subject to the constraint function of x + y = 5

The Lagrange Function would then be equal to:

^{2}

^{2}) λ

^{2}) + λ(x + y – 5)

^{2} + y) λ

** 27. Find: ∫ (3x ^{2} – 7x + 2) dx **

^{3} – (7/2)x^{2} + 2x + C

^{ 3} – (7/2)x^{ 2} + 2x + C

^{3} – 7 + C

** 28. Find**** : ** **∫ [(1/x 2) – 2x -1] dx **

^{-1} – 2 | ln x | + C

** 29. Given: ** z = f (x, y) = x ^{2} – y ^{2} + xy – 5

** Find ∂z/∂x and ∂z/∂y: **

_{ x } (x, y) = 2x + y ; f _{y }(x, y) = -2y + x

_{x } (x, y) = 2x +2 x ; f_{ y }(x, y) = 2y + y

_{x } (x, y) = x + 2x ; f _{y } (x, y) = 2y + x

_{x } (x, y) = 2x + y ; f _{y } (x, y) = 2y + y

** 30. Evaluate:**