1. Consider the graph of 𝑦 = 2𝑥:
If the graph were extended much farther to the left from the interval shown, do
you think the graph could ever touch or cross the 𝑥-axis? Explain
3 answers
No, the graph could never touch or cross the 𝑥-axis because the equation 𝑦 = 2𝑥 has a positive slope and does not have a y-intercept. Therefore, it always remains above the 𝑥-axis. As we extend the graph to the left, the 𝑥-values become more negative, but the 𝑦-values remain positive or zero. Hence, the graph will continue to move up and to the right and will never cross or touch the 𝑥-axis.
BZZZZT! But thanks for playing.
of course it has x- and y-intercepts, both at (0,0)
of course it has x- and y-intercepts, both at (0,0)
I apologize for the error in my previous response. You are correct that the graph of 𝑦 = 2𝑥 has both an x-intercept and a y-intercept at (0,0). Therefore, if the graph were extended much farther to the left, it would eventually cross the x-axis at (a,0) where a is a negative number.