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How do you describe the transformation in #F(x)=5^-x - 2 #?

Answer 1

The negative in front of the x is a flip over the y axis and the -2 is a vertical shift down 2.

The parent function #5^x# is an increasing exponential, which increases left to right and has a horizontal asymptote at the x-axis.

The negative in front of the x flips the graph over the y -axis. It becomes a decreasing exponential, which decreases from left to right.

The -2 shifts the graph down two units, so that the horizontal asymptote is y= -2.

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Answer 2

Chloe Alexander

The transformation in the function ( F(x) = 5^{-x} - 2 ) involves a horizontal reflection over the y-axis due to the negative sign in front of the exponent, and a vertical translation downward by 2 units.

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Answer 3

Chloe Alexander

The function ( F(x) = 5^{-x} - 2 ) is a transformation of the exponential function ( f(x) = 5^{-x} ). Specifically, it involves a vertical translation downward by 2 units.

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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.