Quiz : How Much Do You Know About Evaluating Functions And Their Graphs

The function rule f(x) = 0.25x - 10 represents a linear equation. To find f(5), we substitute 5 for x in the equation and solve for f(5). Plugging in 5, we get f(5) = 0.25(5) - 10 = 1.25 - 10 = -8.75. Therefore, the statement "f(5) = 0" is false.

The given relation is a function because each input value (x-coordinate) corresponds to only one output value (y-coordinate). In other words, there are no repeated x-values in the relation. Therefore, for every x-value, there is a unique y-value, satisfying the definition of a function.

The given function rule is f(x) = 3x - 14. To find f(2), we substitute x = 2 into the function. Thus, f(2) = 3(2) - 14 = 6 - 14 = -8. Therefore, the statement f(2) = -8 is true.

The vertical line test is a method to determine if a relation is a function. If every vertical line intersects the graph at most once, then the relation is a function. In this case, the answer states that the relation passes the vertical line test, indicating that it is a function. Additionally, it is stated that the relation is linear, which means that it can be represented by a straight line.

The correct answer is False because if we substitute x = 3 into the function rule f(x) = 5x - 3, we get f(3) = 5(3) - 3 = 15 - 3 = 12, not -2.

The correct answer is "No, it is not a function at all." The vertical line test is used to determine if a relation is a function. If any vertical line intersects the graph of the relation at more than one point, then the relation is not a function. Since the answer states that it is not a function at all, it means that there are vertical lines that intersect the graph at more than one point. Therefore, the relation fails the vertical line test and is not a function. The question does not provide information about whether the relation is linear or not.

The given relation is not a function because there are multiple inputs (-2 and 2) that are associated with different outputs (3 and 4). In a function, each input can only have one corresponding output.

When x = 0, the value of f(x) is -2.

The function rule f(x) = -2x + 3 is evaluated for the domain {3, -6}. Plugging in 3 for x, we get f(3) = -2(3) + 3 = -6 + 3 = -3. Plugging in -6 for x, we get f(-6) = -2(-6) + 3 = 12 + 3 = 15. Therefore, the range of the function is {3, 15}.

The answer "Yes, but it is not linear" suggests that the relation satisfies the vertical line test, meaning that each vertical line intersects the graph at most once, indicating that it is a function. However, the relation is not linear, meaning that it does not have a constant rate of change.

The given answer states that x can have the values 5, 4, and 6 when f(x) is equal to 3. This means that when the function f is evaluated at x = 5, x = 4, and x = 6, the output is 3. The other options, x = 2 and x = 7, are not included in the answer because they do not satisfy the condition f(x) = 3. Therefore, the correct values for x when f(x) = 3 are x = 5, x = 4, and x = 6.

The domain of a graph refers to all the possible input values or x-values. In this case, since it is stated that the domain is "All real numbers," it means that any real number can be used as an input for this graph.

The range of a graph refers to all the possible output values or y-values. Similarly, since it is stated that the range is "All real numbers," it means that any real number can be obtained as an output from this graph.

Therefore, the correct answer is that the domain and range of the graph are both "All real numbers."

The domain of a graph refers to all the possible input values, or x-values, that the graph can take. In this case, the domain is stated as "all real numbers," which means that there are no restrictions on the x-values.

The range of a graph refers to all the possible output values, or y-values, that the graph can take. In this case, the range is stated as "y > -1 (or equal to)," which means that all y-values must be greater than -1 or equal to -1.

Therefore, the given answer correctly states that the domain is all real numbers and the range is y > -1 (or equal to).

The given answer correctly states that the domain of the graph is x = 3, meaning that the graph only exists at the point x = 3. The range is stated as all real numbers, indicating that the graph can take any y-value. It is also correctly stated that the graph is not a function, as a function must have a unique output for every input, but in this case, multiple y-values can correspond to the same x-value of 3.