Consider the exponential function fx = 3one-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 fx = one-third Superscript x.The function is a shrink of the function fx = 3x.

Answer: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 \(f(x)=(\frac{}1{}{}3{})^{}x{}\) ⇒ True (4th)* Lets revise the form of the exponential function- The general form of the exponential function is \(f(x)=a(b)^{}x{}\)   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 \(f(x)=3(\frac{}1{}{}3{})^{}x{}\)∴ The initial value is 3∴ The growth factor is \(\frac{}1{}{}3{}\)∵ 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 \(\frac{}1{}{}3{}\)# The function shows exponential decay ⇒ True    because the growth factor is less than 1# The function is a stretch of the function \(f(x)=(\frac{}1{}{}3{})^{}x{}\)    ⇒ 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 \(f(x)=(3)^{}x{}\) ⇒ Not true    because the growth factor is not 3