Graph ƒ₁ and ƒ₂ together. Then describe how applying the absolute value function in ƒ₂ affects the graph of ƒ₁.
ƒ₁(x)        ƒ₂(x)
 x²          |x|²

Verified step by step guidance

1. Start by graphing the function \( f_1(x) = x^2 \). This is a standard parabola that opens upwards with its vertex at the origin (0,0). The graph is symmetric about the y-axis.
2. Next, consider the function \( f_2(x) = |x|^2 \). Since \( |x| = x \) when \( x \geq 0 \) and \( |x| = -x \) when \( x < 0 \), the function \( |x|^2 \) simplifies to \( x^2 \) for all real numbers \( x \).
3. Graph \( f_2(x) = |x|^2 \). Notice that it is identical to \( f_1(x) = x^2 \) because \( |x|^2 = x^2 \) for all \( x \). Therefore, the graph of \( f_2 \) is also a parabola opening upwards with its vertex at the origin.
4. Discuss the effect of the absolute value function on \( f_1(x) \). In this case, applying the absolute value function to \( x \) before squaring does not change the graph because squaring a number, whether positive or negative, results in a positive value. Thus, \( f_2(x) \) is the same as \( f_1(x) \).
5. Conclude that the application of the absolute value function in \( f_2(x) \) does not affect the graph of \( f_1(x) \) in this particular case, as both functions result in the same graph: a parabola opening upwards with vertex at the origin.