Discuss how to convert the standard form of the equation of a circle to the general form.

Explanation:

The standard form of the equation of a circle is ...

  (x -h)² +(y -k)² = r² . . . . . . circle centered at (h, k) with radius r

The general form of the equation of a circle will be ...

  Ax² +Bxy +Cy² +Dx +Ey +F = 0 . . . . . A = C for a circle

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The former is converted to the latter by eliminating parentheses, subtracting r² and collecting terms.

  x² +y² -2hx -2ky +(h² +k² -r²) = 0

This shows you that ...

  A = C = 1

  B = 0

  D = -2h

  E = -2k

  F = h² +k² -r²

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In general form, we like to have the coefficients be mutually prime integers and the leading coefficient be positive. That is not always possible, depending on the circle being represented.

the answer is the option b

the range is all real numbers

step-by-step explanation:

we know that

the absolute value parent function is equal to

see the attached figure to better understand the problem

so

a. it is v-shaped > is true

b. the range is all real numbers > is not true

because the range is the > [0,∞)

all real numbers greater than or equal to zero

c. it goes through the origin > is true

d. the domain is all real numbers > is true

step-by-step explanation: