Algebra 2 ! what are the x and y intercepts of the equation? round the answers to the nearest hundredth. y = log(12x + 7) - 3

Step-by-step explanation:

A graphing calculator can show you the intercepts.

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Or you can figure them out.

The y-intercept is where x=0, so is ...

  y = log(12·0 +7) -3 = log(7) -3 ≈ -2.1549 ≈ -2.15

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The x-intercept is where y = 0, so is ...

  0 = log(12x +7) -3

  3 = log(12x +7) . . . . . . add 3

  10^3 = 12x +7 . . . . . . . take the antilog

  993 = 12x . . . . . . . . . . subtract 7

  993/12 = x = 82.75 . . . divide by the coefficient of x

the correct functions are

h(x) = 3x + 2  

g(x) = 2^x

step-by-step explanation:

i proceed to calculate the different values ​​of k (x)

case 1)  k(x) = g(x) ∘ h(x)

g(x) ∘ h(x)=g(h(x))

k(x) = [2]^[3x + > is the option  4. k(x) = 2^(3x + 2 )

case 2)  k(x) = g(x) + h(x)

k(x) = [2^x]+[3x + 2]=2^x+3x+> is the option  1.) k(x) = 2^x + 3x + 2

case 3)k(x) = h(x) ÷ g(x)

k(x) =  [3x + 2]/[2^x]=3x/(2^x)+2/(2^x)=3x*(2^-x)+2^(1-x)

is the option  3.)   k(x) = (3x)2^(-x) + 2^(-x + 1 )

case 4)k(x) = g(x) - h(x)

k(x) =  [2^x]-[3x + 2]=2^x-3x-> is the option  2.) k(x) = 2^x - 3x - 2 

case 5)  k(x) = g(x) × h(x)

k(x) = [2^x]*[3x + > is the option  5.) k(x) = 2^x(3x + 2)

case 6)k(x) = h(x) ∘ g(x)

h(x) ∘ g(x)=h(g(x))

k(x)=3*[2^x]+> is the option  6. k(x) = 3(2^x) +2