Question

G(x) = 3Vx - 5
Find the domain, range, and r and y-intercept. Show your work

Answer 1

To find the domain, range, x-intercept, and y-intercept of the function G(x) = 3Vx - 5, we need to analyze the given equation.

1. Domain:

The domain of a function refers to the set of all possible input values, or x-values, for which the function is defined. In this case, since there are no restrictions or limitations mentioned in the equation, the domain of G(x) is all real numbers (-∞, ∞).

2. Range:

The range of a function refers to the set of all possible output values, or y-values, that the function can produce. For the given function G(x) = 3Vx - 5, since the coefficient of 'x' is positive (3), the function is increasing. This means that as 'x' increases, the value of G(x) also increases. Therefore, the range of G(x) is all real numbers (-∞, ∞).

3. x-intercept:

To find the x-intercept, we set G(x) = 0 and solve for 'x'. So, we have:

3Vx - 5 = 0

3Vx = 5

x = 5 / 3V

Therefore, the x-intercept of the function is x = 5 / 3V.

4. y-intercept:

To find the y-intercept, we set x = 0 in the equation G(x) = 3Vx - 5. So, we have:

G(0) = 3V(0) - 5

G(0) = -5

Therefore, the y-intercept of the function is y = -5.

By following these steps, you should be able to find the domain, range, x-intercept, and y-intercept of the given function. Remember to carefully analyze the equation and apply the appropriate mathematical concepts to obtain accurate results.

Answer 2

- Domain: (-∞, +∞)

- Range: (-∞, +∞)

- x-intercept: (5/3, 0)

- y-intercept: (0, -5)

Explanation:

Domain: The domain of a function refers to the set of all possible input values (x-values) for which the function is defined. In this case, since there are no restrictions or excluded values mentioned, the function is defined for all real numbers. Therefore, the domain is (-∞, +∞).

Range: The range of a function refers to the set of all possible output values (y-values) that the function can produce. In this case, the function is a linear function with a slope of 3 and a y-intercept of -5. As the value of x increases, the value of G(x) also increases. Similarly, as x decreases, G(x) decreases. Therefore, the range of the function is also all real numbers, (-∞, +∞).

x-intercept: To find the x-intercept, we set G(x) equal to 0 and solve for x. So, we have:

0 = 3Vx - 5

3Vx = 5

x = 5/3

Therefore, the x-intercept is (5/3, 0).

y-intercept: The y-intercept is the point at which the graph of the function intersects the y-axis. To find the y-intercept, we substitute x = 0 into the function G(x). So, we have:

G(0) = 3V(0) - 5

G(0) = -5

Therefore, the y-intercept is (0, -5).