Question

Given four functions, which one will have the smallest y-intercept?

f(x) g(x) h(x) j(x)
Blake is tracking his
savings account with
an interest rate of 5%
and a original deposit
of $6.
x g(x)
0 6
1 8
2 12
the function h of x equals 4 to the x power, plus 3 j(x) = 10(2)x

f(x)
g(x)
h(x)
j(x)

Answer 1

The smallest y-intercept is 4 whose function is h(x)

C is correct.

Explanation:

Given four functions, which one will have the smallest y-intercept

For function f(x)

Blake is tracking his savings account with an interest rate of 5% and a original deposit of $6.

`y=6(1+0.05)^x`

`y=6(1.05)^x`

`f(x)=6(1.05)^x`

where, y is final amount and x is number of period.

y-intercept of f(x). Put x=0

`f(0)=6`

y-intercept: (0,6)

For function g(x)

x : 0 1 2

g(x) : 6 8 12

Using table, y-intercept of g(x)

g(0)=6

y-intercept: (0,6)

For function h(x)

`h(x)=4^x+3`

For y-intercept of h(x). Put x=0

`h(0)=4^0+3=4`

y-intercept: (0,4)

For function j(x)

`j(x)=10(2)^x`

For y-intercept of j(x). Put x=0

`j(0)=10(2)^0=10`

y-intercept: (0,10)

Function : f(x) g(x) h(x) j(x)

y-intercept : 6 6 4 10

Hence, The smallest y-intercept is 4 whose function is h(x)

Answer 2

The smallest y-intercept would be of the first function. (0, 6)

Since Blake is starting with $6, that is the y-intercept.

For the function, f(x) = 4^x + 3, the y-intercept is 7.
For the last function, f(x) = 10(2)^x , the y-intercept is 10.

6 is the lowest of 6, 7, and 10.