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.

The graph of f(x) = 10^x 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.

Expert Solution

Consider the parent graph;

f(x) = 10x

Consider the graph is reflected about the-axis, then;

-g(x) = -10x

The graph is shifted upward by 7 units, then, the new function for the parent graph is;

g(x) = -10x + 7.

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

The parent graph g(x) = -10x + 7 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 lesser than 7.

To find the y-intercept set x = 0, as follows:

y = -100 + 7

= -1 + 7

= 6

Therefore, y-intercept is (0, 6).

Junaid answered 10 months ago

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