Question

The graphs of the quadratic function and the exponential function are shown below.




Considering only the domain shown on the graph, over which interval is the value of the exponential function greater than the value of the quadratic function?





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Answer 1

Given : The graphs of the quadratic function y = 2x² and the exponential function y=2ˣ

To Find : Considering only the domain shown on the graph, over which interval is the value of the exponential function greater than the value of the quadratic function

-2.5 ≤ x ≤ 0.75

1  < x ≤ 1.5

-0.5 ≤ x < 1

1  < x   ≤ 2.5

Solution:

from the graph :

y = 2ˣ  is in green  color

y =  2x²  in blue color

for   x = 1

=> y =  2x² = 2(1)² = 2  

   y = 2ˣ= 2¹ = 2  

value of the exponential function =  the value of the quadratic function

at x = 0

   y =  2x² = 2(0)² = 0  

   y = 2ˣ= 2⁰ = 1

1 > 0

=>   value of the exponential function greater than the value of the quadratic function

Hence  x  <  1

x = -0.5

  y =  2x² = 2(-0.5)² =  0.5

   y = 2ˣ= 1/√2 = 0.707

0.707 > 0.5

=>  value of the exponential function greater than the value of the quadratic function

Hence  for   -0.5 ≤ x < 1

 value of the exponential function greater than the value of the quadratic function

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