Question

Which graph represents a reflection of f(x) = 2(0.4)x across the y-axis? On a coordinate plane, an exponential function approaches y = 0 in quadrant 2 and increases into quadrant 1. It crosses the y-axis at (0, 2) and goes through (1, 5). On a coordinate plane, an exponential function decreases from quadrant 3 to quadrant 4 and approaches y = 0 in quadrant 3. It crosses the y-axis at (0, negative 2) and goes through (1, negative 5). On a coordinate plane, an exponential function decreases from quadrant 2 to quadrant 1 and approaches y = 0 in the first quadrant. It goes through the y-axis at (0, 2) and goes through (negative 1, 5). On a coordinate plane, an exponential function increases from quadrant 3 to quadrant 4 and approaches y = 0. It goes through (negative 1, negative 5) and crosses the y-axis at (0, negative 2).

Answer 1

Answer:B

Step-by-step explanation:

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Answer 2

The graph of g(x) is (a) an exponential function approaches y = 0 in quadrant 2 and increases into quadrant 1. It crosses the y-axis at (0, 2) and goes through (1, 5).

The function f(x) is given as:

$f(x) = 2(0.4)^x$

• The rule of reflection over the y-axis is:

$(x,y) \to (-x,y)$

This means that:

$g(x) =f(-x)$

• Substitute -x for x in f(x)

$f(-x) = 2(0.4)^{-x}$

• Substitute the expression for f(-x) in the above equation $g(x) =f(-x)$

$g(x) = 2(0.4)^{-x}$

Hence, the graph of g(x) is graph (a)

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