Understanding Power Functions and Their Graphs

What is a key property of all power function graphs when both X and K are positive?

• They are always linear.

• They contain the point (1, K).

• They are asymptotic to the axes.

• They pass through the point (0, 0).

How do graphs behave when K is negative?

• They become undefined.

• They move to the second quadrant.

• They shift to the fourth quadrant.

• They remain in the first quadrant.

What happens to a power function when X values are negative and the function is undefined?

• The graph becomes a straight line.

• The graph shifts to the third quadrant.

• The function is not plotted for negative X values.

• The graph reflects over the y-axis.

Which of the following describes an even function?

• It passes through the point (0, 0).

• It has origin symmetry.

• It is undefined for negative X values.

• It has y-axis symmetry.

For the function f(x) = 2x^(-3), what is true about its graph?

• It is a linear function.

• It is symmetric around the y-axis.

• It is asymptotic to the axes.

• It passes through the point (2, 1).

How can you determine if a function is odd?

• Check if it has y-axis symmetry.

• Check if f(-x) equals the negative of the original function.

• Check if f(-x) equals the original function.

• Check if it passes through the origin.

What is the K value for the function G(x) = -0.4x^(1.5)?

• 1.5

• -0.4

• 0.4

• -1.5

What happens to the function G(x) = -0.4x^(1.5) when X is negative?

• The function becomes linear.

• The function is undefined.

• The graph shifts to the second quadrant.

• The graph becomes a parabola.

For the function H(x) = -x^(0.4), what is the symmetry of the graph?

• It has origin symmetry.

• It has y-axis symmetry.

• It is symmetric around the x-axis.

• It has no symmetry.

How can the exponent 0.4 be rewritten for the function H(x) = -x^(0.4)?

• As a three-halves fraction.

• As a cube root.

• As a two-fifths fraction.

• As a square root.