Let's analyze the given functions and answer the questions based on the image.

We have four functions to consider:

1. Function 1: Information missing in the visible part.
2. Function 2: Information missing in the visible part.
3. Function 3: $y = 2x + 5$ (slope = 2, y-intercept = 5).
4. Function 4: The slope is $-1$ and the y-intercept is $-4$.

Now, let's answer each question:

(a) Which function's graph is the least steep?

• The steepness of a line is determined by the absolute value of the slope. The smaller the absolute value, the less steep the graph is.

  • Function 3 has a slope of 2.
  • Function 4 has a slope of $-1$, which has an absolute value of 1.

  Therefore, Function 4 is the least steep because $| -1 | = 1$ is smaller than 2.

(b) Which functions have graphs with slopes less than $-2$?

• The condition is that the slope should be less than $-2$. None of the visible slopes (2 and -1) meet this criterion.

  • Function 3 has a slope of 2 (greater than -2).
  • Function 4 has a slope of $-1$ (greater than -2).

  So, none of the visible functions (Function 3 or Function 4) have slopes less than $-2$.

(c) Which function has the graph with the greatest y-intercept?

• The y-intercept is where the graph crosses the y-axis (when $x = 0$).

  • Function 3 has a y-intercept of 5.
  • Function 4 has a y-intercept of $-4$.

  Since 5 is greater than $-4$, Function 3 has the greatest y-intercept.

Would you like further details on this or to clarify anything? Here are 5 related questions you might find helpful:

1. What is the relationship between slope and steepness in linear functions?
2. How do you find the slope of a line given two points?
3. Can the y-intercept affect the steepness of a graph?
4. How do positive and negative slopes affect the direction of a line?
5. How can we graph a line given the slope and y-intercept?

Tip: Always remember that the slope of a line determines both its steepness and direction. The greater the absolute value of the slope, the steeper the line!