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Chapter 3: Q. 75 (page 157)

In Problems 75鈥�80, for the given functions f and g,

(a) Graph fand gon the same Cartesian plane.

(b) Solve localid="1647272470729" fx=gx.

(c) Use the result of part (b) to label the points of intersection of the graphs of fand g.

(d) Shade the region for which fx>gx,that is, the region below f and above g.

fx=2x-1,gx=x2-4.

Short Answer

Expert verified

(a) The graph of fxandgx.

(b)x=3,x=-1.

(c) The point of intersection is 3,5and-1,5.

(d) The shaded region for fx>gx.is

Step by step solution

01

Part (a) Step 1. Given information

It is given thatfx=2x-1,gx=x2-4.We need to graphfandgon the same cartesian plane.

02

Step 2. Draw the graph

03

Part (b) Step 1. Given information

It is given thatfx=2x-1,gx=x2-4.We need to solvefx=gx.

04

Step 2. Simplify

fx=gx.

2x-1=x2-4.

x2-2x-3=0.

x=2卤-22-4路1路-32路1.

=2卤162.

=2卤42.

x=2+42andx=2-42.

x=3. x=-1.

The values of the functionfandgare equal whenx1=3,x2=-1.

05

Part c Step 1. Given information

It is given that fx=2x-1,gx=x2-4.We need to use the result of part (b) to label the point of intersecting.

06

Step 2. Simplify

When x1=3,y=2路3-1鈬�y=5.

When x2=-1,y=2路-1-1鈬�y=-3.

So, the point of intersection is3,5and-1,-3.

07

Part d Step 1. Given information

It is given thatfx=2x-1,gx=x2-4.We need to shade the region for whichfx>gx.

08

Step 2. Shade the region

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Most popular questions from this chapter

Graph the function fby starting with the graph of y=x2and using transformations (shifting, compressing, stretching, and/or reflection). Verify your results using a graphing utility.

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Graph the function fby starting with the graph of y=x2and using transformations (shifting, compressing, stretching, and/or reflection). Verify your results using a graphing utility.

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