HSF.IF.B.4 Tutor Intake — Key Features of Graphs

Complete the definition: The x-intercept of a function $f$ is a value of
$x$ where $f(x) =$   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   .

A graph shows a company's monthly profit $P(x)$ in dollars, where $x$ is the
number of months since the business opened. The graph crosses the x-axis at
$x = 4$.

What does this x-intercept represent in context?

The temperature $T(t)$ in degrees Fahrenheit on a winter night is decreasing
from $t = 6$ pm to $t = 2$ am, but $T(t) > 0$ throughout that interval.

Which statement is correct?

A graph of $f(x)$ has three peaks. The leftmost peak reaches $y = 8$, the
middle peak reaches $y = 15$, and the rightmost peak reaches $y = 11$.

Which of the following is true?

A business's weekly profit in dollars is modeled by $P(x) = 3x - 120$, where
$x$ is the number of units sold.

Find the x-intercept of $P$. Enter the number of units at the break-even point.

A graph of $g(x)$ is described as follows:

• From $x = -3$ to $x = 1$, the graph falls from left to right.
• From $x = 1$ to $x = 5$, the graph rises from left to right.
• The graph is below the x-axis for $-3 < x < 4$ and above the x-axis for $x > 4$.

On which interval is $g$ both decreasing and negative?

The function $h(t) = -5t^2 + 20t$ models the height (in meters) of a soccer
ball at time $t$ seconds after it is kicked.

The ball reaches its relative maximum height at $t = 2$ seconds.

What is the maximum height, in meters? (Enter a number.)

A linear function $f(x) = 4x - 20$ is graphed in the coordinate plane.

What is the y-intercept of $f$? (Enter the y-value as a number.)

A graph of $f(x) = x^2 - 4$ is shown in a small window from $x = -3$ to
$x = 3$. In the window, the graph appears to level off at the right edge
near $y = 5$.

A student says: "The end behavior is that $f(x)$ approaches 5 as $x$
increases, because that's where the graph ends."

What is wrong with this reasoning?