How do you graph #f(x) =abs(2x+3)#?

1 Answer
Apr 29, 2018

Answer:

#" "#
Please read the explanation.

Explanation:

#" "#
#color(green)("Step 1"#

Construct a table of values with Input: #color(red)(x#

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Values are obtained for the graphs:

#y=|x|#

#y=|2x|#

#y=|2x+3|#

You can now analyze how the computed values reflect visually on their respective graphs.

#color(green)("Step 2"#

Consider #color(blue)(y=a|x-h|+k#

This will help understand how transformations will work.

#Vertex: (h,k)#

Graph of #y=|x|#

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This is the Parent Graph.

#Vertex: (0,0)#

#color(green)("Step 3"#

Graph of #y=|2x|#

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#Vertex: (0,0)#

#color(green)("Step 4"#

Graph of #y=|2x+3|#

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Let us find the #Vertex: #

Let #bx - h =0#

#rArr 2x+3=0#

Subtract 3 from both sides.

#rArr 2x+cancel 3-cancel 3=0-3#

#rArr 2x = -3#

Divide both sides by #2#

#rArr (2x)/2 = -3/2#

#rArr (cancel 2x)/cancel 2 = -3/2#

#rArr x= -3/2#

#Vertex: (h.k)#

Hence, #Vertex: (-3/2,3)#

Axis of Symmetry :#x=-3/2=-1.5#

Domain is all possible x values: #(-oo, oo)#

Range: # [0,oo)#

Horizontal Shift:

#k=3# shifts #3# units to the left.

Hope it helps.