Question

Consider the functions ​g(x)equals2xplus1 and ​h(x)equals2xplus2 for the domain 0less thanxless than5.
a. Without evaluating or graphing the​ functions, how do the ranges​ compare?
b. Graph the two​ functions, and describe each range over the given interval.
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Part 1
a. The minimum and maximum values in the range of​ h(x) should be
  
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▼
times
greater than
less than
the minimum and maximum values in the range of​ g(x).
​(Type a whole​ number.)

Answer 1

a. 1 greater than

b. Since g(x)=2x+1 and h(x)=2x+2 are straight lines with slope 2 and h(x)=g(x)+1, h is the graph of g shifted up by 1. For 0 < x < 5:
- g(0)=1 and g(5)=11, but 0 and 5 are not included, so Range(g) = (1, 11).
- h(0)=2 and h(5)=12, so Range(h) = (2, 12).

On the graph both are lines of slope 2 on 0<x<5; g has open endpoints at (0,1) and (5,11), h has open endpoints at (0,2) and (5,12).