Mathematics, 21.01.2020 21:31 mantooth

The graph of g(x) is transformed from its parent function, f(x). apply concepts involved in determining the key features of a rational function to determine the domain and range of the function, .

a. what is the domain of the function, g(x)?
b. what is the range of the function, g(x)?

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Answer from: bo4isbad

Domain of a function is defined by the x-values (Input values) and Range is defined by the y-values (output values).

Domain of the given function 'g' → (-∞, -4)∪(-4, ∞)

Range of the given function 'g' → (-∞, 0)∪(0, ∞)

Function given in the function,

g(x) = $\frac{1}{x+4}$

For x = -4, given function is not defined [Since, g(x) has the vertical asymptote at x = -4]

For y = 0, function 'g' is not defined [Since, g(x) has the horizontal asymptote at y = 0]

Therefore, domain of the function will be all x- values except x = -4 Or (-∞, -4)∪(-4, ∞) and range of the function will be all y-values except y = 0 Or (-, 0)∪(0, ∞).

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Answer from: GingerSnaps

G(x) = 1 / (x+4) is a modification of the "parent function" f(x) = 1/x, whose domain is the set of all real numbers other than x = 0 (cannot divide by zero). Similarly, the range of f(x) is "all real numbers other than y=0."

g(x) has the same graph as does f(x), with the exception that the graph of f(x) has been moved (translated) 4 units to the left. Whereas x could not = 0 before, now x cannot equal -4, because then the denom. of g(x) would be zero.

In this transformation the range remains the same from f(x) to g(x).
The graph of g(x) is transformed from its parent function, f(x). apply concepts involved in determin

The graph of g(x) is transformed from its parent function, f(x). apply concepts involved in determin

Answer from: Quest

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

Answer from: Quest

idk

step-by-step explanation:

The vector 6,-5 is reflected across the y=x and the resulting matrix is dilated by a scale of -1.5

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