If f(x) = 2x + 3 then Δy/Δx = 2 and g(x) = 2² +3 then Δy/Δx = 2.33.
The correct answer is option A.
f(x) has a rate of change of 2
g(x) has a rate of change of 2.33
So g(x) is growing faster
Let f(x) = 2x + 3 and g(x) = 2² +3
Let, ∆y /∆x denotes the ratio of y change and x change when x change exists relatively large.
If f(x) = 2x + 3
Δy/Δx = [f(3) - f(0)]/3 - 0
f(3) [tex]= 2*3+3 = 9[/tex]
f(0) [tex]= 2*0+3 = 3[/tex]
[f(3) - f(0)]/3 - 0 = (9 - 3)/3
= 6/3 = 2
g(x) = 2² +3
Δy/Δx = [g(3) - g(0)]/3 - 0
[tex]$= (2^3 +3)-(2^0 +3)/3[/tex]
[tex](2^3 +3)-(2^0 +3) = 7[/tex]
[tex](2^3 +3)-(2^0 +3)/3[/tex] = 7/3 = 2.33
Therefore, the correct answer is option A.
f(x) has a rate of change of 2
g(x) has a rate of change of 2.33
So g(x) is growing faster
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