Which is the graph of the piecewise function f(x)? f(x)= {-x+1, x<0, x+1,x>0
2 answers:
Answer:
The graph is attached.
Step-by-step explanation:
The first piece of the function, f(x) = -x+1, has a y-intercept of 1 and a slope of -1. This means it will be decreasing by 1 for every increase in x until it hits the y-intercept of 1.
The second piece of the function, f(x) = x+1, has a y-intercept of 1 and a slope of 1. This means it will start at the y-intercept of 1 and increase by 1 for every increase in x.
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Answer:
or
or equivalently:
or
Step-by-step explanation:
To express the Fahrenheit temperature <em>as a linear function of the Celsius temperature</em>, F(c), we can proceed as follows.
We can use here <em>the two-point form</em> <em>equation</em> of a line:
[1]
We are asked to express the <em>Fahrenheit temperature</em> as a function of <em>Celsius temperature</em>, so the independent variable, in this case, is <em>x</em> (Celsius temperature) and the dependent variable is <em>y</em> (Fahrenheit temperature).
When temperature is zero degree Celsius (), the Fahrenheit temperature is 32 (
).
When the Celsius temperature is 100 (), the corresponding Fahrenheit temperature is 212 (
).
Then, using [1], we have:
.
It could be also be written as:
=
, as it commonly appears in books.
Then <em>the Fahrenheit temperature express as a linear function of the Celsius temperature, F(c</em>) is ( solving the equation for <em>y </em>) :
or
.
Or equivalently:
or
We can check this using the given values from the question:
For 0 Celsius degrees, the Fahrenheit temperature is:
= 32 Fahrenheit degrees.
For 100 Celsius degrees, the Fahrenheit temperature is:
= 212 Fahrenheit degrees.