Let fx 2x2 3x 1 and h x 2 x2 3 x 1 The graph of h can

Let f(x) = 2x^2 + 3x + 1 and h (x) = 2 (-x)^2 + 3 (-x) + 1. The graph of h can be derived from the graph of f by: Shifting the graph of f to the left one unit Shifting the graph of f down one unit Reflecting the graph of f across the x-axis Reflecting the graph of f across the y-axis None of these Let f(x) = 2x^2 + 3x + 1 and h (x) = 2(-x)^2 + 3(-x) + 1. The graph of h can be derived from the graph of f by; Shifting the graph of f to the left one unit Shifting the graph of f down one unit Reflecting the graph of f a across the x-axis Reflecting the graph of f across the y-axis None of these Let f (x) = 5x^4 - 7x + 1 and g(x) = 5x^4 +7x + 1. The graph of g can be derived from the graph of f by: Reflecting the graph of f across the x-axis Reflecting the graph of f across the y-axis Reflecting the graph of f across the x-axis first then across the y-axis None of the above Let f(x) = 3x^4 - 7x^2 + 1. Find the function that is the reflection of f(x) about y-axis.

Solution

5] f(x) = 2x² + 3x + 1 and g(x) = 2(- x)² + 3(-x) + 1

from g(x), we see that x has been replaced by \' - x\'

so, the graph will be reflected about the y-axis.

6] f(x) = 5x⁴ - 7x + 1 and g(x) = 5x⁴ + 7x + 1

since ( - x)⁴ = x⁴, we can rewrite g(x) as: g(x) = 5( - x)⁴ - 7( - x) + 1

which is identical to f(x) but x has been replaced by \' - x\'

therefore g(x) is a reflection of f(x) about y axis.

7] f(x) = 3x⁴ - 7x² + 1

if a function is a reflection about y axis, g(x) = 3( - x)⁴ - 7(- x)² + 1 = 3x⁴ - 7x² + 1 = f(x).