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lesya [120]
2 years ago
8

If this is the graph of f(x) = a^(x+h) + k then

Mathematics
2 answers:
Natali [406]2 years ago
5 0

Answer:

The domain is (-∞,∞) and range is (k,∞)

Step-by-step explanation:

The graph is given as a^(x+h)+k.

When x =0, we have f(x) a^h+k= y intercept

Consider the exponential function y = a^x.

This is defined for domain all real numbers and range = (0,infinity) for all positive a.

This function is transformed into our function by horizontal shift of h units to left and vertical units of k units up.

i.e. Y = y-k and X = x-h

Since x has domain as set of all real numbers X also set of real numbers

So domain is (-∞,∞)

Since range of original graph is (0,∞), we have Y minimum value as k and max as infinity.

Range = (k,∞)


svet-max [94.6K]2 years ago
4 0

The correct option is \boxed{\bf option (D)} i.e., domian is \boxed{\bf (-\infty,\infty)} and the range is \boxed{(k,\infty)}.

Further explanation:

It is given that the function is f(x)=a^{(x+h)}+k.

First we consider the exponential function f(x)=a^{x}, the domain of this function is (-\infty,\infty) and range is (0,\infty).

The domain of a function is defined as all possible value of x which satisfy the function.

The range of a function is defined as the all possible outcome of the function that is the possible values of y.

The given graph of the function f(x)=a^{(x+h)}+k is the transformation of the graph of the function f(x)=a^{x}.

If a constant is added to the argument of the function, the graph of the function shifts to the left if the constant is positive i.e., f(x+a) and it shifts to the right if the constant is negative i.e., f(x-a).

If a constant is added to a function, the graph of the function shifts vertically upwards if the constant is positive i.e., f(x)+a and it shifts vertically downwards if the constant is negative i.e., f(x)-a.

In the given function constant h is added to the argument of the function f(x)=a^{x}, so the graph of the function shifts to the left.

And also in the given function constant k is added to the function f(x)=a^{x}, so the graph of the function shifts vertically upwards.

Therefore, the domain of this transformed function f(x)=a^{(x+h)}+k will remain the same (-\infty,\infty) as the original function f(x)=a^{x} as all the value of x satisfy this transformed function and the range of the function will become (k,\infty) as the minimum value of y is k and maximum is \infty.

Now we will check from the given option that which option is correct step by step.

Option (A):

In option (A) the domain is given as (h,\infty) and the range is (-\infty,\infty) which is not matching with the above answer, so the option (A) is incorrect.

Option (B):

In option (B) the domain is given as (-\infty,\infty) and the range is (h,\infty) whichis not matching with the above answer, so the option (B) is also incorrect.

Option (C):

In option (C) the domain is given as (h,\infty) and the range is (k,\infty) whichis not matching with the above answer, so the option (C) is also incorrect.

Option (D):

In option (D) the domain is given as (-\infty,\infty) and the range is (k,\infty) which is matching with the above answer, so the option (D) is correct.

Learn more

1. Problem on coordinates of triangles after rotation brainly.com/question/7437053

2. Problem on transformation of the triangle when rotated about origin brainly.com/question/2992432

Answer details:

Grade: High school

Subject: Mathematics

Topic: Shifting of Curve

Keywords: Function, range, domain, f(x)=a^(x+h)+k, constant, vertically, f(x)=a^(x), argument, graph, left, exponential, maximum, argument, shifting, translation, transformation, exponential function.

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