Consider the exponential function f(x) = 3(one-third) superscript x and its graph.
on a coordinate plane, an exponential function decreases from quadrant 2 into quadrant 1 and approaches y = 0. it crosses the y-axis at (0, 3) and goes through (1, 1).
which statements are true for this function and graph? select three options.
the initial value of the function is one-third.
the growth value of the function is one-third.
the function shows exponential decay.
the function is a stretch of the function f(x) = (one-third) superscript x.
the function is a shrink of the function f(x) = 3x.

The growth value of the function is One-third ⇒ True (2nd)

The function shows exponential decay ⇒ True (3rd)

The function is a stretch of the function ⇒

True (4th)

Step-by-step explanation:

* Lets revise the form of the exponential function

- The general form of the exponential function is

  where "a" is the initial amount and "b" is the growth factor

- If b > 1, then f(x) is exponential growth function

- If 0 < b < 1, then f(x) is exponential decay function

* Lets solve the problem

- The exponential function

∴ The initial value is 3

∴ The growth factor is

∵ The growth factor is less than 1

∴ f(x) is exponential decay function

* Lets chose the true statements

# The initial value of the function is One-third ⇒ Not true

   because the initial value is 3

# The growth value of the function is One-third ⇒ True

   because the growth factor is

# The function shows exponential decay ⇒ True

   because the growth factor is less than 1

# The function is a stretch of the function

   ⇒ True

  because stretched vertically means multiply f(x) by constant greater

  than 1 and 3 is greater than 1

# The function is a shrink of the function ⇒ Not true

   because the growth factor is not 3

(x3 + 6x2 + 2x - 6) • (x - 1)

step-by-step explanation:

polynomial long division :

3.2     polynomial long division

dividing :   x4+5x3-4x2-8x+6

                              ("dividend")

by         :     x-1     ("divisor")

dividend     x4   +   5x3   -   4x2   -   8x   +   6

- divisor   * x3     x4   -   x3            

remainder         6x3   -   4x2   -   8x   +   6

- divisor   * 6x2         6x3   -   6x2        

remainder             2x2   -   8x   +   6

- divisor   * 2x1             2x2   -   2x    

remainder               -   6x   +   6

- divisor   * -6x0               -   6x   +   6

remainder                     0

quotient :   x3+6x2+2x-6   remainder:   0