Question

Determine the equations of the following graphs

Answer 1

Hello,

Explanation:

a)

`y=a^x*b+c\\\\if\ x- > -\infty,\ y- > -1 \ \Longrightarrow\ c=-1\\if\ x=0\ y=1\ \Longrightarrow\ 1=b-1\ \Longrightarrow\ b=2\\if\ x=1\ y=5 \ \Longrightarrow\ a*2-1=5\ \Longrightarrow\ a=3\\\\\boxed{y=2*3^x-1}\\`

b)

`f(x,y)=(x-a)(y-b)-k=0\ since\ hyperbola\`

c)

It is parabola

y=k*(x-3)(x+3)

(1,24) is a point of the parabola:

24=k*(1²-9) => k=-3

`\boxed{y=-3(x^2-9)}\\`