Anyone
a linear function and an exponential function are shown below.
over which interval does the growth rate of the exponential function exceed the growth rate of the linear function?
a x< 1
b 0 is less than equal to x is less than or = to 1
c 1 is less than or = to x is less than or = to 2
d x > 2

D is correct. x>2 the growth rate of the exponential function exceed the growth rate of the linear function.

Step-by-step explanation:

We are given a linear function and an exponential function in graph.

We need to find interval when growth rate of the exponential function exceed the growth rate of the linear function.

Option A) When x<1

Growth rate of linear function = 2

Growth rate of Exponential function = 0.75

When x<1 , growth rate of exponential function is less than linear function.

Option B) When 0≤x≤1  

Growth rate of linear function = 2

Growth rate of Exponential function = 1

When 0≤x≤1  , growth rate of exponential function is less than linear function.

Option C) When 1≤x≤2

Growth rate of linear function = 2

Growth rate of Exponential function = 2

When 1≤x≤2  , growth rate of exponential function is equal to linear function.

Option D) When x>2  

Growth rate of linear function = 2

Growth rate of Exponential function = 4

When x>2  , growth rate of exponential function is exceed the growth rate of  linear function.

Thus, x>2 the growth rate of the exponential function exceed the growth rate of the linear function.

step-by-step explanation:

f(x)=2x^2 -1 

translation is a function transformation that transform the function in a way of translating. by translating the function its graph is moved  up an down. moving the function f(x) 2 units to the left will be the new function g(x) with the equation: g(x)=f(x+2)=2(x+2)^2 -1