Answer:
3. The correct option is A.
4. The correct option is C.
5. The correct option is C.
6. The correct option is B.
Step-by-step explanation:
3.
The given function is
[tex]f(x)=\frac{3}{2}\cdot (\frac{4}{5})^x[/tex]
[tex]lim_{x\rightarrow -\infty}f(x)=lim_{x\rightarrow -\infty}\frac{3}{2}\cdot (\frac{4}{5})^x[/tex]
[tex]lim_{x\rightarrow -\infty}f(x)=\frac{3}{2}\cdot (\frac{4}{5})^{-\infty}=\infty[/tex]
The function approaches to ∞ as x approaches to -∞.
[tex]lim_{x\rightarrow \infty}f(x)=lim_{x\rightarrow \infty}\frac{3}{2}\cdot (\frac{4}{5})^x[/tex]
[tex]lim_{x\rightarrow \infty}f(x)=\frac{3}{2}\cdot (\frac{4}{5})^{\infty}=0[/tex]
The function approaches to 0 as x approaches to ∞.
Therefore option A is correct.
4.
The given function is
[tex]g(x)=-6(5)^x[/tex]
The exponential function is in the form of
[tex]f(x)=ab^x[/tex]
If a<0, then f(x) is a negative function and if a>0, then f(x) is a positive function.
If |b|>1, then f(x) is a increasing function and if |b|<1, then f(x) is a decreasing function.
Since a=-6<0 and b=5>1, therefore f(x) is a negative and increasing function.
Option C is correct.
5.
From the given graph it is noticed that the graph passing through the points (-1,-8) and (1,-2).
We have to find the slope of graph from -1 to 1.
[tex]m=\frac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]
Slope of function form -1 to 1 is
[tex]m=\frac{f(1)-f(-1)}{1-(-1)}=\frac{-2-(-8)}{1-(-1)}=\frac{6}{2}=3[/tex]
Therefore option C is correct.
6.
The y-intercept is 2 it means at x=0, the value of y is 2.
[tex]f(x)=3^{2x}=3^{2(0)}=3^0=1[/tex]
[tex]g(x)=3^x+1=3^0+1=1+1=2[/tex]
[tex]h(x)=3^x+2=3^0+2=1+2=3[/tex]
[tex]j(x)=3*2^x=3*2^0=3[/tex]
Since g(x) has y-intercept 2, therefore option B is correct.
