# Sketch Curves: y=5x^(3/4), y=-2x^(-3/2)

• Harmony
In summary, the given equations are y=5x^(3/4) and y=-2x^(-3/2). These are not quadratic functions and cannot be represented by circles, parabolas, ellipses, or hyperbolas. To graph them, one can manipulate the exponents and calculate y for different values of x in their respective domains.
Harmony

## Homework Statement

Sketch the curves with the following equations:
a) y=5x^(3/4)
b) y=-2x^(-3/2)

## Homework Equations

The general equation of curves (circles, parabola, ellipse, hyperbola)

## The Attempt at a Solution

It seems to me that this question is not exactly a coordinate geometry question. At first, I thought this is a parametric equation, but parametric equation use t instead of y. Then, I thought of substituting x with some other things. But that fails as well. (The fraction power make it not rational to be substituted by x^2, x^3 and so on.) The equation doesn't resemble general equation circles, parabola, ellipse, or hyperbola.

How should I attempt this question? Is equation of curves really useful to solve this question?

There are other basic graphs of functions, so these would be some of them. Perahps it would be easier for you to re-write the fractional exponents. Well, that would be if you have gotten to that (or know how to).

I will let you know though, both of those equations don't resemble a circle, parabola, ellipse, or hyperbola.

As I said, try manipulating the exponents.

As pointed out, these are not quadratic functions and so their graphs are not conic-sections (circle, ellipse, hyperbola, parabola). Basically, just calculate y for a number of x values and draw a smooth curve through the points. As radou said, you'd better check the domains.

## 1. What is the equation for the sketch curve y=5x^(3/4)?

The equation for the sketch curve y=5x^(3/4) is a power function with an exponent of 3/4, where x is the independent variable and y is the dependent variable. It represents a curve that starts at the origin and increases rapidly as x increases.

## 2. What is the equation for the sketch curve y=-2x^(-3/2)?

The equation for the sketch curve y=-2x^(-3/2) is also a power function, but with a negative coefficient and an exponent of -3/2. This results in a curve that starts at the origin and decreases rapidly as x increases.

## 3. How do you graph the sketch curves y=5x^(3/4) and y=-2x^(-3/2)?

To graph these sketch curves, you can plot a few points by substituting different values of x into the equations and then connect the points with a smooth curve. Alternatively, you can use a graphing calculator or software to plot the curves accurately.

## 4. What is the domain and range of the sketch curves y=5x^(3/4) and y=-2x^(-3/2)?

The domain of both sketch curves is all real numbers except for x=0, as the equations are undefined at that point. The range of y=5x^(3/4) is all positive real numbers, while the range of y=-2x^(-3/2) is all negative real numbers.

## 5. How can I use the sketch curves y=5x^(3/4) and y=-2x^(-3/2) in real life?

These sketch curves may represent real-life situations such as population growth or decay, where x represents time and y represents the number of individuals. They can also be used in economics to model supply and demand curves. Additionally, they can be used as tools for problem-solving and analyzing data in various fields of science and engineering.

• Precalculus Mathematics Homework Help
Replies
4
Views
525
• Precalculus Mathematics Homework Help
Replies
10
Views
793
• Precalculus Mathematics Homework Help
Replies
23
Views
1K
• Precalculus Mathematics Homework Help
Replies
18
Views
1K
• Precalculus Mathematics Homework Help
Replies
2
Views
1K
• Precalculus Mathematics Homework Help
Replies
1
Views
1K
• Precalculus Mathematics Homework Help
Replies
3
Views
1K
• Precalculus Mathematics Homework Help
Replies
3
Views
744
• Precalculus Mathematics Homework Help
Replies
10
Views
1K
• Precalculus Mathematics Homework Help
Replies
11
Views
3K