Identity the function that reflects fx 14x3 7x2 6 across

Identity the function that reflects f(x) = 14x^3 - 7x^2 + 6 across the y-axis and shifts it 6 units up. h(x) = 14x^3 - 74x^2 h(x) = 1x^3 - 7x^2 h(x) = 14x^3 + 7x^2 + 12 h(x) = -14x^3 - 7x^2 + 12

Solution

Given function is f(x) = 14x³ -7x² + 6

Need to find the function that reflects f(x) across the y-axis and shifts it 6 units up.

Reflects across the y-axis means f(-x).

f(-x) = 14(-x)³ -7(-x)² + 6

f(-x) = -14x³ -7x² + 6

Shifting f(-x), 6 units up means f(-x) + 6

h(x) = f(-x) + 6

=  -14x³ -7x² + 6 + 6

=  -14x³ -7x² + 12

Therefore, h(x) = -14x³ -7x² + 12

So, 4^th option is the correct answer.