Find x-coordinate of the vertex of parabola

Question

Assignment:

1) State the domain of the following and provide a brief explanation for your

a. f(x)=√x+4
b. g(x)=2x-1/x-7
c. h(x)=3x²+5x-3
d. l(x)=2x+3
e. m(x)=3/x²+7

2) Suppose the graph of is shifted to obtain each the following graphs. What is the equation of the function, g(x), for each graph? Write your answers in terms of x2 and/or x.

a)

b)

3) Consider the following graph of y = f(x).

a) If h(x) = f(x) + 2, what would the new coordinates of P be after the shift? Give answer in (x, y) form.

b) If , what would the new coordinates of P be after the reflection? Give answer in (x, y) form.

4) Consider the function .

f(x)=x²+4x+1

a) Find h, the x-coordinate of the vertex of this parabola.

b) Substitute the two integers immediately to the left and right of h into the function to find the corresponding y. Fill in the following table. Make sure your x-values are in increasing order in your table.

c) Use MS Excel to graph the function by plotting the points found in the table in part b.

5) Find the equations of the horizontal and vertical asymptotes for the following. Type none if the function does not have an asymptote.

a)f(x)=2x+3/x+2

Horizontal:
Vertical:

b) g(x)=5x/x2-1

Horizontal:
Vertical:

c)

Horizontal:
Vertical:

d)

Horizontal:
Vertical: