Final answer:
A horizontal shrink with |c| > 1 on a function's graph results in a narrower, compressed appearance towards the y-axis. For a given value of y, the corresponding x-values get closer, but the general shape and slope of the graph remain unchanged.
Step-by-step explanation:
When a horizontal shrink with |c| > 1 is applied to the graph of a function, the graph compresses horizontally toward the y-axis. This means that for each value of y, the x-values of the points on the graph become closer together — effectively, the graph looks narrower rather than wider.
Consider a basic function f(x). If we apply a horizontal shrink by a factor of c (with |c| > 1), we create a new function g(x) = f(cx). In this new function, each x-value that used to produce a certain y-value on the graph of f(x) is divided by c in the graph of g(x), causing the x-values to 'squeeze' toward the y-axis.
For example, suppose we have a linear function with a positive slope, represented by y = a + bx, where b > 0. If a horizontal shrink of 2 is applied, we would now have y = a + b(2x), effectively doubling the input x-values and causing the graph to compress horizontally. As a result, the graph's slope appears steeper due to the shrink, even though the actual rate of increase or decrease in y for each unit increase in x remains unchanged.