6. At x = 3, we can substitute into the function: [tex]y = (-3)^{\frac{2}{3}x} = (-3)^{2} = 9[/tex]
7. The y-intercept is the value of y when x = 0. Substituting x = 0:
[tex]y = 12(4^{x}) \\ y = 12(4^{0}) \\ y = 12[/tex]
8. The base function is [tex]y = 6^{x}[/tex], and this is vertically stretched by 2 (as implied by the multiplier of [tex]6^x[/tex]), 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.
