How to answer these two questions ?

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1 Answer
MathFact-orials.blogspot.com
Aug 28, 2017

See below:

Explanation:

a

We're looking for the #y#-intercept - which means that #x=0#:

#h(x)=3+abs(x-2)#

#h(0)=3+abs(0-2)#

#h(0)=3+abs(-2)#

#h(0)=3+2=5#

b

The range is the list of #y# values associated with a domain. Let's find the highest value first.

By the graph, the range is at the maximum at #h(7)#:

#h(7)=3+abs(7-2)#

#h(7)=3+5=8#

To find the minimum value, we first need to know at what #x# value it occurs. We can do that by observing that the absolute value function will only return positive values - the smallest value it can return is 0. So where will #abs(x-2)=0#? At #x=2#.

#:. h(2)=3+abs(2-2)#

#h(2)=3#

#:. "Range": 3<=h(x)<=8#

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