Question

are functions 1 and 2 the same? explain.
function 1: ( y = 3(x + 5) )
function 2: y equals three times x, plus 5.
a no. ( 3(x + 5) = 15x ) and \three times x, plus 5\ would be ( 3x + 5 ).
b yes, ( 3(x + 5) ) and \three times x, plus 5\ are both equal to ( 15x ).
c yes, ( 3(x + 5) ) and \three times x, plus 5\ are both equal to ( 3x + 5 ).
d no. ( 3(x + 5) = 3x + 15 ) and \three times x, plus 5\ would be ( 3x + 5 ).

Explanation:

Step1: Expand Function 1

Using the distributive property \( a(b + c)=ab + ac \), for \( y = 3(x + 5) \), we get \( y=3x+3\times5 = 3x + 15 \).

Step2: Translate Function 2 to Algebraic Form

"Three times \( x \), plus 5" translates to \( y = 3x+5 \).

Step3: Compare the Two Functions

Function 1 simplifies to \( 3x + 15 \) and Function 2 is \( 3x + 5 \). So they are not the same. Now check the options:

• Option A: \( 3(x + 5)=15x \) is wrong (correct is \( 3x + 15 \)).
• Option B: Both equal to \( 15x \) is wrong.
• Option C: Both equal to \( 3x + 5 \) is wrong (Function 1 is \( 3x + 15 \)).
• Option D: Correctly states \( 3(x + 5)=3x + 15 \) and Function 2 is \( 3x + 5 \), so they are not the same.

Answer:

D. No. \( 3(x + 5)=3x + 15 \) and "three times \( x \), plus 5" would be \( 3x + 5 \).