Answer:
True statements:
- B) Only f(x) and h(x) have x-intercepts.
- C) The minimum of h(x) is less than the other minimums.
- E) The maximum of g(x) is greater than the other maximums.
Step-by-step explanation:
y-intercept
The y-intercept of a function is the point at which the graph intersects the y-axis, having an x-coordinate of zero, (0, y).
Since the table provides the value of all functions when x = 0, each of the three functions has a y-intercept.
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x-intercepts
The x-intercept(s) of a function is the point(s) at which the graph intersect(s) the x-axis, having an y-coordinate of zero, (x, 0).
Only functions f(x) and h(x) have x-intercepts, as they are the only functions that have values of zero in the provided table.
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Minimum value
The minimum value of a function is the function's lowest value among all the points listed in the table. Therefore:
Minimum of f(x) = -14
Minimum of g(x) = 1/49
Minimum of h(x) = -28
So, the minimum of h(x) is less than the other minimums as -28 < -14 < 1/49.
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Range
The range of a function is the set of all possible output values. Therefore:
Range of f(x) = {-14, -7, 0, 7, 14}
Range of g(x) = {1/49, 1/7, 1, 7, 49}
Range of h(x) = {-28, -7, 0}
Comparing the number of distinct y-values, we can see that f(x) and g(x) each have 5 distinct values, while h(x) has only 3 distinct values.
Therefore, f(x) and g(x) have more values in their ranges compared to h(x).
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Maximum value
The minimum value of a function is the function's greatest value among all the points listed in the table. Therefore:
Maximum of f(x) = 14
Maximum of g(x) = 49
Maximum of h(x) = 0
So, the maximum of g(x) is greater than the other maximum as 49 > 14 > 0.
