The point 𝐴 is on the graph of 𝑦 is equal to 𝑓 of 𝑥. The graph is transformed to give the graph of 𝑦 is equal to 𝑓 of negative 𝑥 plus
eight. When the graph is transformed, the point 𝐴 is mapped to the point 𝐵. The coordinates of point 𝐴 are four, negative three. What are the coordinates of point 𝐵?
Remember we use this function notation just to tell us that we’ve got an equation for
𝑦 that is in terms of 𝑥. That equation could be 𝑦 is equal to 𝑥 squared or 𝑦 is equal to four 𝑥 cubed. But since we don’t know what the function is, we use 𝑓 of 𝑥 instead.
Two transformations have been applied to this function. The first is given by 𝑓 of negative 𝑥. 𝑓 of negative 𝑥 represents a reflection of the original graph in the 𝑦-axis. Secondly, the function has had eight added to it. This represents a translation by the vector zero, eight. That’s eight units up.
Let’s consider then what each of these transformations does to the coordinate four,
negative three. First, there’s that reflection in the 𝑦-axis. When we reflect the point four, negative three in the 𝑦-axis, its image lies at the
point negative four, negative three.
Remember an image must be the exact same distance away from the mirror line as the
original object. Here, it was four units away from the 𝑦-axis. The 𝑦-coordinate negative three remains unchanged.
Next, the graph is translated by the vector of zero, eight. That’s eight units up. This means that the 𝑥-coordinate now remains unchanged and the 𝑦-coordinate
increases by eight. Negative three plus eight is five. The coordinates of point 𝐵 are, therefore, negative four, five.