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Find examples that support or refute your classmates’ answers to the discussion question.
Provide additional similarities and differences between functions and linear equations. Challenge
your classmates by providing more intricate examples of nonlinear functions for them to solve
To test a function you can use the vertical line test, If the vertical line crosses the line in 2 or
more points, then the equation is not a function . Create an equation of a nonlinear function and
provide two inputs for your classmates to evaluate.
Student1:
What similarities and differences do you see between
functions and linear equations studied in Ch. 3?
Functions are often described by graphs, whether or not an
equation is given. To use a graph in an application, we note that
each point on the graph represents a pair of values. As in chapter
three called ordered pairs. Also the f(x) symbol can be represented
by the y symbol.
What about linear equations ?
Linear equations are represented by a line and the graph of a non
linear function is not a line.
Are all linear equations functions?
All linear equations will meet the requirement of a function, by using
the horizontal line test.
That´s not true, vertical lines have a linear equation (x=a) and the
graph does not pass the vertical line test (x=a is not a function)
Is there an instance when a linear equation is not a function?
There are no instances where a linear equation is not a function. As
long as it passes the linear line test it is a function.
This is wrong, as we said vertical lines have a linear equations but is
not a function
Support your answer:
To test a function you can use the vertical line test, If the vertical
line crosses the line in 2 or more points, then the equation is not a
function .
If x=a is a vertical line and we select the point x=a , the vertical line crosses the graph of x=a in
infinitely many points so vertical lines does not pass the vertical line test so vertical lines are not
functions
Create an equation of a nonlinear function and provide two inputs
for your classmates to evaluate.
3 x ² +4 ² = 16
2x ² - 3y ² = 5
Here are 2 nonlinear equations but there aren´t inputs
We can modify the answer:
Equation: f(x)=3x^2+16, inputs: 2 and 3
Answer: f(2)=3(22)+16=12-16=-4;
f(3)= 3(32)+16=27-16=11
Student 2: A common trait for both functions and linear equations is that
they both can be considered to be equations, but a function consists of a
domain and a range, that corresponds to exactly one member. Another
difference between the two would be that functions don't have to look
like straight lines when you graph them, but linear equations are straight
lines.
Linear equations like y=ax+b (a  0) have a domain and range too (real
numbers), I agree with the second part, functons don´t have to look like
straight lines.
Not every linear equation is a function. For example, vertical lines are not
functions, since for any input value there are multiple output values.
Vertical lines fail the "vertical line" test, which says that a vertical line
must cross a function at most one time.
I agree with this part too, we can say that vertical lines are the only kind
of linear equations that are not a function.
Example: f(x) = x^2 - 3
Inputs 0 and -10
Problem is right.
We can add a problem:
f(x)=x7-1, inputs 2 and -2
Solve Problem: f(x)= x+3
This is a linear equation, but is not clear what we have to solve