A student was asked to decide whether the function below is linear or nonlinear using both a table and a graph. he said the function is nonlinear because the rate of change is constant and the graph of the function is not a line. Decide whether the function is linear or nonlinear using both a table and a graph. What mistake might the student have made?
y=-x ^2
Complete the table of values for the function.
x y
-2 blank
-1 blank
0 blank
1 blank
2 blank
To complete the table of values for the function y = -x^2, let's substitute the given x-values into the function and calculate the corresponding y-values.
x y
-2 -(-2)^2 = -(-2)(-2) = -4
-1 -(-1)^2 = -(-1)(-1) = -1
0 -(0)^2 = -(0)(0) = 0
1 -(1)^2 = -(1)(1) = -1
2 -(2)^2 = -(2)(2) = -4
Therefore, the completed table of values for the function is:
x y
-2 -4
-1 -1
0 0
1 -1
2 -4
Based on the table of values, we can observe that as the x-values increase or decrease, the corresponding y-values do not increase or decrease at a constant rate. Therefore, the function y = -x^2 is nonlinear.
Regarding the student's mistake, they incorrectly stated that the rate of change is constant for the function. In reality, the rate of change varies as x increases or decreases, resulting in a nonlinear relationship.
A student was asked to decide whether the function below is linear or nonlinear using both a table and a graph. he said the function is nonlinear because the rate of change is constant and the graph of the function is not a line. Decide whether the function is linear or nonlinear using both a table and a graph. What mistake might the student have made?
y=6 ^2
Complete the table of values for the function.
x y
-2 blank
-1 blank
0 blank
1 blank
2 blank
To complete the table of values for the function y = 6^2, let's substitute the given x-values into the function and calculate the corresponding y-values.
x y
-2 6^2 = 36
-1 6^2 = 36
0 6^2 = 36
1 6^2 = 36
2 6^2 = 36
Therefore, the completed table of values for the function is:
x y
-2 36
-1 36
0 36
1 36
2 36
Based on the table of values, we can observe that as the x-values increase or decrease, the corresponding y-values remain constant at 36. Therefore, the function y = 6^2 is a linear function.
Regarding the student's mistake, they incorrectly stated that the rate of change is constant for the function. In reality, the value of y remains constant regardless of the change in x. The student may have made an error in interpreting the function or calculating the y-values in the table.
A student was asked to decide whether the function below is linear or nonlinear using both a table and a graph. he said the function is nonlinear because the rate of change is constant and the graph of the function is not a line. Decide whether the function is linear or nonlinear using both a table and a graph. What mistake might the student have made?
y=x ^2
Complete the table of values for the function.
x y
-2 blank
-1 blank
0 blank
1 blank
2 blank
To complete the table of values for the function y = x^2, let's substitute the given x-values into the function and calculate the corresponding y-values.
x y
-2 (-2)^2 = 4
-1 (-1)^2 = 1
0 (0)^2 = 0
1 (1)^2 = 1
2 (2)^2 = 4
Therefore, the completed table of values for the function is:
x y
-2 4
-1 1
0 0
1 1
2 4
Based on the table of values, we can observe that as the x-values increase or decrease, the corresponding y-values do not increase or decrease at a constant rate. This indicates a nonlinear relationship between the x and y values.
The student's statement that the function is nonlinear because the rate of change is constant is incorrect. In the function y = x^2, the rate of change, or the slope, of the function increases as the x-values move away from zero. The student may have mistakenly assumed that since the rate of change is constant in certain sections of the graph (such as between x = -2 and x = -1 as well as between x = 1 and x = 2), the entire function is linear. However, when considering the overall relationship between x and y, it is clear that the function y = x^2 is nonlinear.
Use the graph of the function shown to the right to find all values of x such that g(x)=7
x=
(Use a comma to separate answers as needed.)