Can someone help me with assigning functions with corresponding graphs? How should one proceed to make it easily without a ton of calculations (this kind of exercise I need to do within 5 minutes)?
Assign graphs to functions
x^(-9/5), x^(-3/2), x^(-1), x^(-3/5),x^(-1/2), x^(2/5), x^(3/8), x^(3/7), x^3, x^4
This is a terrible question. At the level of your graphic, I can't easily tell the difference between the second, third, and fifth graphs. One doesn't usually allow taking fractional powers of negative numbers when the denominator is even, so $x^{-\frac 32}$ and $x^{\frac 38}$ should not extend left of the $y$ axis. There is no graph that matches $x^4$ (plot it-it looks roughly like a parabola but flatter on the bottom). The second, third, and fifth correspond to negative exponents, because they go infinite at $x=0$. The fourth is symmetric around the $y$ axis, so its numerator is even, and the vertical approach to $x=0$ indicated that the exponent is less than $1$, so it must be $x^{\frac 25}$. The first is $x^3$ with it being negative for negative $x$ and horizontal approach to $x=0$