Question 916237: How to graph polynomials. Where do I start? I am lost on these two problems. I don't know what I need to do in order to figure out the graph of:
f(x) = 4 log(base 4)(x + 8)
and
h(x) = (2x+6)(x–3)^2 (x+1)^3
Is there any way to tell what a graph will look like before starting?
Thank you in advance!
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! figure out the graph of:
f(x) = 4 log(base 4)(x + 8)
f(x) = 4[log(x+8)/log(4)]
Sketch the basic curve, y = log(x)
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Shift that graph 8 units to the left because of the (x+8).
Multiply each y-value by 7/log(4) = 6.64 to get:
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and
h(x) = (2x+6)(x–3)^2 (x+1)^3
f(0) = 6(9)(1) = 54:: So plot (0,54)
Roots at -3, + 3, and -1:: So plot (-3,0),(-1,0),(3,0)
Graph does not pass thru (3,0)
Graph passes thru (-1,0)
Highest power is x*x^2*x^3 = x^6::
y goes to +oo as x goes to -oo
y goes to +oo as x goes to +00
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Cheers,
Stan H.
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