The graph of f(x) = 6.5x is reflected about the y-axis and stretched vertically by a factor of 7. What is the equation of the new function, g (x)? State its y-intercept, domain, and range.

Expert Solution

Consider the parent function;

f(x) = 6.5x

Since, the graph is reflected about the y-axis,

Therefore;

g(-x) = 6.5-x

The graph is stretched vertically by a factor of 7, then, the new function for the parent graph is;

g(-x) = 7(6.5)-x

The characteristic of the graph of the parent graph in form f(x) = bx, is written as follows:

The parent graph g(-x) = 7(6.5)-x is;

1. One-to-one function.

2. Horizontal asymptote is y = 0.

3. Domain of the graph is set of all real numbers, that is (-∞, ∞).

4. Range is set of all real numbers greater than 0.

5. Its y-intercept is (0, 7).

Umair answered 1 year ago

The graph of f(x) = 10x is reflected about the x-axis and shifted upward 7 units. What is the equation of the new function, g(x)? State its y-intercept, domain, and range.

Graph the function f(x) = 3.5(2)x. State the domain and range and give the y-intercept.

The graph of ?(?) = 5 ^−? is reflected about the y-axis and compressed vertically by...

The graph of ?(?) = 5 ^−? is reflected about the y-axis and compressed vertically by a factor of 1/3. Determine the equation of the new function, ?(?). Also state the y-intercept, domain, and range of ?(?).

Graph the function f(x) = 4 (1/8)x and its reflection about the y-axis on the same axes, and give the y-intercept.

The graph of a function y = g(x) on the domain −8 ≤ x ≤ 8...

The graph of a function y = g(x) on the domain −8 ≤ x ≤ 8 consists of line segments and semicircles of radius 2 connecting the points (−8, 0), (−4, 4), (0, 4), (4, 4), (8, 0). (a) What is the range of g? 0 < y < 60 ≤ y ≤ 4 0 ≤ y ≤ 20 < y < 40 ≤ y ≤ 6 (b) Where is the function increasing? (Select all that apply.) −8 ≤ x ≤...

The deﬁnition of a (well-deﬁned) function f : X → Y . Meaning of domain, range,...

The deﬁnition of a (well-deﬁned) function f : X → Y . Meaning of domain, range, and co-domain

For the following exercises, use the information about the graph of a polynomial function to determine the function. Assume the ...The y-intercept is (0, 1). There is no x-intercept. Degree is 4. End behavior: as x → −∞, f(x) → ∞, as x → ∞, f(x) → ∞.

The y-intercept is (0, 1). There is no x-intercept. Degree is 4. End behavior: as x → −∞, f(x) → ∞, as x → ∞, f(x) → ∞.

please graph the function f(x)=(x-2)/(x-1) by finding the domain the x and y intercepts the vertical...

please graph the function f(x)=(x-2)/(x-1) by finding the domain the x and y intercepts the vertical asymptotes the horizontal asymptotes the intervals of increase and decrease the local mins/max the intervals of concavity the inflection point(s) as an ordered pair

State the domain, vertical asymptote, and end behavior of the function f(x) = log5 (39 − 13x) + 7.

If a function f(x) is odd about a point, say (a,0), on the x-axis what exactly...

If a function f(x) is odd about a point, say (a,0), on the x-axis what exactly does this mean? How would you relate f(x values to left of a) to f(x values to right of a)? Similarly, if a function f(x) is even about a point, say (a,0), on the x-axis what exactly does this mean? How would you relate f(x values to left of a) to f(x values to right of a)? I understand what is meant by odd...

Question