Question 1:

Find an equation for each line:

(a) L1 goes through the point (1, -2) and is parallel to x = 3y + 3 .

(b) L2 goes through the point (4, 1) and is perpendicular to y = 5x + 1.

2

Show work and express the equation as slope-intercept form y=mx+b for full credit.

Question 2:

Let f(x) = 2|x 1| + 1.

(a) Graph the function. Label the axes clearly for full credit. (6 pts)

(b) Determine the range of the function. (1 pt)

(c) List the interval(s) on which the function is increasing. (1 pt)

(d) Find the zeros of the function if any exist. (1 pt)

(e) Find the absolute extrema if they exist. Determine if the absolute extrema are minimum or maximum.(1 pt)

Show work and rationale for full credit

Question 3:

Let f(x)= 3x² 18x + 2:

(a) Convert f(x) into standard form a(x)² + k. (6 pts)

(b) Find the range of the function. (1 pt)

(c) Identify the vertex. (1 pt)

(d) Identify the axis of symmetry. (1 pt)

(e) Determine whether the vertex yields a relative and absolute maximum or minimum. (1 pt)

Show work and rationale for full credit.

Question 4:

Solve the inequality. Write answer using interval notation

(a) 10x x² < 25

(b) 5x + 6 < x²

Show work and rationale for full credit.

Question 5:

Let (x)=x(x2)²(x+1).

(a) Find the real zeros of (x) and their corresponding multiplicities. (3 pts)

(b) Use the information from part (a) along with a sign chart to provide a rough sketch of the graph of the polynomial. (4 pts for sign chart and 2 pts for graph)

(c) Based on part (b), which interval is the relative minimum located in? (1 pt)

Show work and rationale for full credit.