SOLUTION: The figure shows the graphs of f(x) = x3 and g(x) = ax3. What can you conclude about the value of a? a. a < –1 b. –1 < a < 0 c. 0 < a < 1 d. 1 < a

Algebra ->  Rational-functions -> SOLUTION: The figure shows the graphs of f(x) = x3 and g(x) = ax3. What can you conclude about the value of a? a. a < –1 b. –1 < a < 0 c. 0 < a < 1 d. 1 < a      Log On


   

Question 107482: The figure shows the graphs of f(x) = x3 and g(x) = ax3.
What can you conclude about the value of a?
a. a < –1
b. –1 < a < 0
c. 0 < a < 1
d. 1 < a
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29+=+x3 and g%28x%29+=+ax3
are you sure this is what you need x3 or you need x%5E3
I guess that cubic function is what you need:

f%28x%29+=+x%5E3 and g%28x%29+=+ax%5E3 to see what changes we get if we chaging a
here is the graph of f%28x%29+=+x%5E3:

Solved by pluggable solver: Graph of a cubic equation





now, watch the graph if

a.a+%3C+-1
we can take a+=+-3 and see what is different if we compare it to previous
Solved by pluggable solver: Graph of a cubic equation





now, watch the graph if
b. –1 < a < 0......let a+=+-0.7, do you see any difference?
Solved by pluggable solver: Graph of a cubic equation






now, watch the graph if
c. 0 < a+< 1......let a+=+%2B0.7, do you see any difference?

Solved by pluggable solver: Graph of a cubic equation





now, watch the graph if
d. 1 < a.......let a+=+5
Solved by pluggable solver: Graph of a cubic equation






If a getting smaller and smaller then+0, graph is getting closer and closer to from x-axis to y-axis and lies in II and IV quadrant.
Let see the graph for a=-0.000001which is very close to 0…….it is almost straight line which tend to lie on x-axis but still goes through II and IV quadrant.

Solved by pluggable solver: Graph of a cubic equation





Let see the graph for a=-+44which is very distant from 0…….it is almost straight line which tend to lie on y-axis

Solved by pluggable solver: Graph of a cubic equation





If a getting greater and greater then 0, graph is getting closer and closer to from x-axis to y-axis and lies in II and IV quadrant.
Let see the graph for a=0.000001which is very close to 0…….it is almost straight line which tend to lie on x-axis but still goes through I and III quadrant.
Solved by pluggable solver: Graph of a cubic equation





Let see the graph for a=44 which is very distant from 0…….it is almost straight line which tend to lie on y-axisbut still goes through I and III quadrant.
Solved by pluggable solver: Graph of a cubic equation