Consider the function h(x) = - 2(1/3)* . Determine the following features of h(x).
the a- term: ?
y- intercept: ?
the common ratio: ?
x- intercept: ?
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To determine the features of the given function h(x) = -2(1/3)x:
a-term: The a-term refers to the constant factor of the function. In this case, the a-term is -2.
y-intercept: The y-intercept is the value of the function when x = 0. To find the y-intercept, substitute x = 0 into the function:
h(0) = -2(1/3)(0)
= 0
Therefore, the y-intercept is 0.
common ratio: The common ratio is not relevant in this given function, as it is linear (with a power of 1). Common ratio is typically used in geometric sequences or exponential functions.
x-intercept: The x-intercept is the value of x where the function equals zero. To find the x-intercept, set h(x) = 0 and solve for x:
-2(1/3)x = 0
x = 0
Therefore, the x-intercept of the function is 0.
To determine the features of the function h(x) = -2(1/3)x, let's break down the equation and find the values of each feature:
1. The a-term (coefficient of x): The a-term represents the coefficient of the variable x in the equation. In this case, the a-term is -2(1/3), which simplifies to -2/3. Therefore, the a-term of h(x) is -2/3.
2. The y-intercept: The y-intercept is the value of y when x is equal to 0. To find the y-intercept, we substitute x = 0 into the equation h(x) = -2(1/3)x. By doing so, we get: h(0) = -2(1/3)*0 = 0. Hence, the y-intercept of h(x) is 0.
3. The common ratio: The common ratio refers to the value that multiplies x in each term of the function. In this case, the common ratio is -2(1/3), which simplifies to -2/3. Thus, the common ratio of h(x) is -2/3.
4. The x-intercept: The x-intercept is the value of x when y is equal to zero, or in other words, the value(s) of x for which h(x) = 0. To find the x-intercept, we set h(x) = 0 and solve for x. In this case, we have -2(1/3)x = 0. To cancel out the -2/3, we can multiply both sides of the equation by -3/2. This gives us -3/2 * -2(1/3)x = -3/2 * 0, which simplifies to x = 0. Therefore, the x-intercept of h(x) is x = 0.
To summarize:
- The a-term of h(x) is -2/3.
- The y-intercept of h(x) is 0.
- The common ratio of h(x) is -2/3.
- The x-intercept of h(x) is x = 0.