Consider the function h(x) = - 2(1/3)* . Determine the following features of h(x). (( can you check and help me with my work))
the a- term: ?
y- intercept: there is none
the common ratio: 1/3
x- intercept: -2
To determine the features of the function h(x) = -2(1/3)x, let's break it down step by step.
1. The a-term: The a-term refers to the coefficient multiplying the variable x. In this case, the a-term is -2(1/3) or -2/3.
2. The y-intercept: The y-intercept is the point where the graph intersects the y-axis, which is the point where x = 0. To find the y-intercept, substitute x = 0 into the equation h(x) = -2(1/3)x: h(0) = -2(1/3)(0) = 0. Therefore, there is no y-intercept in this equation.
3. The common ratio: The common ratio represents the multiplication factor between consecutive terms in a geometric sequence. However, in h(x) = -2(1/3)x, there is no common ratio because it is a linear equation, not a geometric sequence.
4. The x-intercept: The x-intercept represents the point where the graph intersects the x-axis, which is the point where y = 0. To find the x-intercept, substitute y = 0 into the equation h(x) = -2(1/3)x: 0 = -2(1/3)x. Solving for x, we have -2/3 * x = 0. Multiplying both sides by 3/-2, we get x = 0. Therefore, the x-intercept is x = 0.
In summary:
- The a-term is -2/3.
- There is no y-intercept.
- There is no common ratio.
- The x-intercept is x = 0.