Question

function notation:

1. find the value of f(2)
2. find the value of f(-1).

1)
2)

Explanation:

Step1: Find \( f(2) \)

To find \( f(2) \), we look at the graph of the function \( f(x) \). We find the point on the graph where \( x = 2 \). From the graph, when \( x = 2 \), we move up (or down) to the corresponding \( y \)-value. The graph is a parabola opening upwards with vertex at the origin \((0,0)\). The equation of this parabola appears to be \( f(x)=x^{2} \) (since it's a standard parabola \( y = x^{2} \)). So when \( x = 2 \), \( f(2)=2^{2}=4 \). We can also verify this by looking at the graph: at \( x = 2 \), the \( y \)-coordinate is 4.

Step2: Find \( f(-1) \)

To find \( f(-1) \), we look at the graph where \( x=- 1 \). Using the equation \( f(x)=x^{2} \) (since the parabola is symmetric about the \( y \)-axis), when \( x=-1 \), \( f(-1)=(-1)^{2}=1 \). From the graph, at \( x = - 1 \), the \( y \)-coordinate is 1.

Answer:

1. \( \boldsymbol{4} \)
2. \( \boldsymbol{1} \)