Find the exponential function that passes through the points (1, 3) and (2, 9). a) y = 12x b) y = 9x c) y = 6x d) y = 3x

D

Step-by-step explanation:

An exponential function which crosses through (1,3) and (2,9) will have a base of 3 since the y values are multiples of 3.

3^1 = 3

3^2 = 9

This means that the function is y = 3^x.

y = 3x

Substitute the two points into the equation y = abx, giving 3 = ab1 and 9 = ab2.

Since a = a, then  

3

b1

=  

9

b2

, rearranged yields 3b2 = 9b1 → 3b2 − 9b = 0 → b(3b − 9) = 0

Thus, b = 0 or b = 3.

A curve of exponential function never drop below the x-axis, ignore any values of b that are less than or equal to zero.

Therefore, insert b = 3 into  

3

b1

= a and  

9

b2

= a → a = 1 for both equations.

y = abx

y = (1)(3x)

y = 3x

. + λrh() e 1 1 2 4 4 4 4 4 3 4 4 4 4 4 + th−1(− s(x)2 dx ω + λrh−1() e 2 1 2 4 4

step-by-step explanation:

for this pair of functions g(x)=x-2 and f(x)=|x| is (g o f)(a)= |a| -2

step-by-step explanation:

g(x)=x-2

f(x)=|x|

(g o f)(a)=?

(g o f)(x)=g(f(x))

(g o f)(x)=g(|x|)

(g o f)(x)=|x|-2

(g o f)(a)=|a|-2