Question

Which of the following is true about the function y= 4 * 3tothepowerofx

a.
the function decreases
c.
if the value of x increases by 1, the value of y will triple.
b.
the function has a y-intercept of (0, 3)
d.
the function contains the point (1, 4)

Answer 1

Only true statement for function f(x) =
`4(3^(x))` is c. if the value of x increases by 1, the value of y will triple.

Explanation:

a. the function decreases

f(x) =
`4(3^(x))` , For value of x<1 function decreases and for x>1 function increases . False statement .

c. if the value of x increases by 1, the value of y will triple.

For value of x increases by 1 we have ,
`f(x) = 4(3^(x+1)) = 4(3^(x))(3) = f(x) (3) = y(3)` . True statement.

b. the function has a y-intercept of (0, 3)

At y intercept x=0, f(x) =
`4(3^(x))` ,
`f(0) = 4(3^(0)) = 4` . Function has a y-intercept of (0,3). False statement.

d. the function contains the point (1, 4)

At x=1,
`f(1) = 4(3^(1)) = 12` . Function contains (1,12) not (1,4) . False statement.