Question

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6: evaluate the exponential function y= -3^(2/3)^x when x=3
7: find the y-intercept of the function y=12 (4)^x
8:what are the shifts of the function y=2 (6)^x+2-5
9:does the exponential function y=3^(3/4 )^x-1 represent or growth.
PLEASE HELP THIS IS DUE AT MIDNIGHT

Answer 1

6. At x = 3, we can substitute into the function:
`y = (-3)^{(2)/(3)x} = (-3)^(2) = 9`

7. The y-intercept is the value of y when x = 0. Substituting x = 0:


`y = 12(4^(x)) \\ y = 12(4^(0)) \\ y = 12`

8. The base function is
`y = 6^(x)`, and this is vertically stretched by 2 (as implied by the multiplier of
`6^x`), shifted left by 2 units (because of the exponent being x+2), and shifted down by 5 units (as shown by the -5 term).

9. This represents decay, since the exponential function's base is 3/4, and this has an absolute value < 1. Bases with absolute value > 1 imply growth.