Math 121, Practice Questions for Chapter 2
1. (a) Find the distance between the points (โ3,2) and (9,โ3).
(b) find the midpoint of the line segment with endpoints (3,5) and (โ5,2).
2. (a) Determine the center and radius of the circle whose equation is x2+y2+10x+4y+20 = 0.
(b) Write the equation of a circle whose center is (โ5,1) and passes through the point (3,1).
(c) Find the equation of a circle that has diametral endpoints of (0,0) and (6,8). (Hint: the
center is the midpoint of the diametral endpoints).
3. Let f(x)=2x2+ 7 and g(x) = |xโ1|, find
(a) (fโฆg)(โ5) (b) (gโฆf)(x) (c) (fg)(0) (d) (f+g)(0)
4. Let f(x)=4x2โ3x, find the difference quotient
f(x+h)โf(x)
h
5. Sketch the graph of f(x) = |x+ 3| โ 2 and find intervals where fis (a) increasing; (b)
decreasing. Is fone-to-one?
6. Determine the domains of the following functions.
(a) f(x) = x+ 3
(x+ 2)โ16 โx2.
(b) g(x) = โxโ4
(c) h(x) = โ4โx
(d) k(x) = 3(xโ1)
(x+ 2)(xโ11)
7. (a) Find the slope-intercept form of the line through the points (โ1,3) and (4,โ7).
(b) Find the slope-intercept form of the line that passes through the point (โ3,โ7) and is
perpendicular to the line 2x+ 5y= 10.
(c) Find the slope-intercept form of the line that passes through the point (โ3,โ7) and is
parallel to the line 2x+ 5y= 10.
8. (a) Write the quadratic function f(x) = โ3x2+ 4xโ5 in standard form by completing the
square. Using that information, sketch the graph of f(x).
(b) Find the vertex of the quadratic function f(x) = 3x2โ6x+11, and find the range of f(x).
(c) Find the maximum of the quadratic function f(x) = โ3x2+ 3x+7 and then find its range.
(d) Find the range of the quadratic funciton f(x) = x2โ10x+ 3. Does this function have a
maximum or a minimum? If so, find it.
1
