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Given #f(x)=2(3x+4)-6#, how do you find the y intercept?

Answer 1

Isaiah Anthony

Simplify the equation to get #6x+2#, meaning the #y#-int. is #(0,2)#.

The equation in the question has not yet been simplified down yet. We want to get it into slope-intercept form, or

#y=mx+b#

So we multiply out #2(3x+4)# and get

#y = 6x+8 - 6#

Now we add in the #-6# and our equation should look like

#y=6x+8-6#

We know that #8-6# is #2#, so our #b# value, i.e. the #y#-intercept, is #2# and #m# (the slope) is #6#.

The final product should look like:

#y=6x+2#

Hence, the #y#-intercept is #(0,2)#.

Hope this helped.

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Answer 2

Jameson Allen

To find the y-intercept of a function ( f(x) ), you set ( x ) to zero and solve for ( y ). In this case, with the function ( f(x) = 2(3x + 4) - 6 ), when ( x = 0 ), you have:

[ f(0) = 2(3 \times 0 + 4) - 6 ]

[ f(0) = 2(4) - 6 ]

[ f(0) = 8 - 6 ]

[ f(0) = 2 ]

So, the y-intercept is at the point (0, 2).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.