Question
Which of the exponential functions below has a y-intercept of 2?
a. f(x)= 3^2x
b. g(x)= 3^x +1
c. h(x)= 3^x+2
d. j(x)= 3*2^x
a. f(x)= 3^2x
b. g(x)= 3^x +1
c. h(x)= 3^x+2
d. j(x)= 3*2^x
Answers
GPT 3.5
To find the y-intercept of an exponential function, we substitute x=0 into the function and solve for y.
a. f(x) = 3^(2x)
f(0) = 3^(2*0) = 3^0 = 1
b. g(x) = 3^x + 1
g(0) = 3^0 + 1 = 1 + 1 = 2
c. h(x) = 3^x + 2
h(0) = 3^0 + 2 = 1 + 2 = 3
d. j(x) = 3 * 2^x
j(0) = 3 * 2^0 = 3 * 1 = 3
From the options given, the exponential function with a y-intercept of 2 is g(x) = 3^x + 1, so the correct answer is (b).
a. f(x) = 3^(2x)
f(0) = 3^(2*0) = 3^0 = 1
b. g(x) = 3^x + 1
g(0) = 3^0 + 1 = 1 + 1 = 2
c. h(x) = 3^x + 2
h(0) = 3^0 + 2 = 1 + 2 = 3
d. j(x) = 3 * 2^x
j(0) = 3 * 2^0 = 3 * 1 = 3
From the options given, the exponential function with a y-intercept of 2 is g(x) = 3^x + 1, so the correct answer is (b).