Question

Discussion Topic

In Algebra, we learn about many types of functions. These functions vary from simple to complex. Think about the different types of functions we’ve explored so far (linear, quadratic, and exponential). What features do they share, and how are they unique?

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Answer 1

Answer:

every equation has an unique solution we can find the unknown values which help in various ways to our daily life

Answer 2

Answer:

Step-by-step explanation: A function is a mathematical relationship between inputs and outputs. Functions can be simple or complex.

There are three main types of functions: linear, quadratic, and exponential.

The linear, quadratic and exponential functions are unique and it is shown through the following points.

• Linear functions  have constant first differences. Quadratic functions have constant second differences. Exponential functions have a constant ratio.
• A linear function forms a line, a quadratic function forms a parabola and an exponential function forms a curve that grows steeper over time.
• Linear equations in standard form : y= mx + c, quadratic equations in standard form :y = ax² + bx + c and exponential equations of the form y = a(b)ˣ.
• When using general equations, the exponents determine the identity of the function. A linear equation has no exponent, a quadratic equation has a highest exponent of two, and an exponential equation has a variable in the exponent.

Similarities of linear, quadratic and exponential equations:

• Linear equations are similar to quadratic equations by linear having a visible pattern in the y values, like quadratic equations.

• Quadratic equations are similar to exponential functions by having a curve in the graph. A parabola of course begins to form a curve after its vertex, and an exponential graph  begins to curve right after x₀.

• Linear equations are similar to exponential equations by both having to increase at a same rate as it starts at.

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