Answered

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The table shows three unique functions.
THE TABLE IS SHOWN IN THE ATTACHED IMAGE

Which statements comparing the functions are true? Select three options.

Only f(x) and h(x) have y-intercepts.
Only f(x) and h(x) have x-intercepts.
The minimum of h(x) is less than the other minimums.
The range of h(x) has more values than the other ranges.
The maximum of g(x) is greater than the other maximums.

The Table Shows Three Unique Functions THE TABLE IS SHOWN IN THE ATTACHED IMAGE Which Statements Comparing The Functions Are True Select Three Options Only Fx A class=

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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.

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