Question

Select all of the true statements for the following exponential function.

X: -1, 0, 1
Y: 1/3, 1/2, 3/4

f(x)= __ (__)^x+ ___

Answer 1

Explanation:

we can use the data points to write a system of equations to solve for the values of a and b in the general exponential function of the form f(x) = a(b)^x.

Using the data points, we get:

f(-1) = 1/3 = a(b)^(-1)

f(0) = 1/2 = a(b)^0 = a

f(1) = 3/4 = a(b)^1 = ab

Solving for a and b, we get:

a = 1/2

b = 3/4a = 3/4(1/2) = 3/8

Therefore, the exponential function that matches the given data points is:

f(x) = (3/8)^x + 1/2

Now we can evaluate the statements:

The base of the exponential function is 3/8. (True)

The function is decreasing. (False - since the base is between 0 and 1, the function is actually increasing)

The y-intercept of the function is (0, 1/2). (True)

The function passes through the point (2, 9/16). (False - the function is only defined for x = -1, 0, 1)

The function is concave up. (True)