To begin a power function’s formula is f(x) = kx^P. In the formula, k and p are considered constants. Power function graphs shapes can take on many shapes. The “k” in the formula has nothing to do with the shape of the graph. The “k” is responsible for the expansion or compression of the function vertically. The “p” portion of the formula is what has control of the actual shape of the graph. Depending on if the exponent is an odd or even number makes a difference on how the shape of the graph will turn out. An example can be shown through the Desmos activity.

In this Desmos graph, the two formulas used is y=3x^8 and y=8x^2. As you can see the even exponent gives the graph a u-shape, this is also called a parabola. Due to the fact that the graph goes symmetrically up the y-axis. This is a result of the nonnegative function values of both formulas.

As for this Desmo graph, one can notice how the shape of the two graph is different than the previous one. The reason being the exponents of these two formulas are odd. The shape of this graph is considered a chair shape. The formula for these two graphs is y=4x^3 and y=7x^13.

Two power function I found a bit harder to classify were Y= 1/x and y = x squared. I’ve read on Wiley plus that these power functions are considered are in the category Asymptotes and Limit Notation, but the whole technique to graph and solve is still a little blurry. I can’t really decipher the formula… I guess that might be my biggest problem. The formula is written below.

I think the power functions and should be considered special cases because the graph shape comes out a straight diagonal (x^1) and horizontal (x^0) lines. As shown in the graph below.

Is there a more specific word for a chair shape graph?

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This is a great description of power functions. Later in the semester, we’ll talk about the asymptotes and limit notation you’re describing in your post. In any case, nice work!

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