Question

question 24 (02.05 mc) the table represents the linear function f(x), and the equation represents the linear function g(x). x f(x) 0 1 2 9 4 17 g(x)=3x + 1 compare the y - intercepts and slopes of the linear functions f(x) and g(x) and choose the answer that best describes them. (1 point) the slope of f(x) is less than the slope of g(x). the y - intercept of f(x) is equal to the y - intercept of g(x). the slope of f(x) is less than the slope of g(x). the y - intercept of f(x) is greater than the y - intercept of g(x). the slope of f(x) is greater than the slope of g(x). the y - intercept of f(x) is equal to the y - intercept of g(x). the slope of f(x) is less than the slope of g(x). the y - intercept of f(x) is greater than the y - intercept of g(x).

Explanation:

Step1: Find the slope of f(x)

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Using the points $(0,1)$ and $(2,9)$ from the table of $f(x)$, we have $m_f=\frac{9 - 1}{2-0}=\frac{8}{2}=4$.

Step2: Find the y - intercept of f(x)

The y - intercept is the value of $y$ when $x = 0$. From the table of $f(x)$, when $x = 0$, $f(x)=1$, so the y - intercept of $f(x)$ is 1.

Step3: Analyze g(x)

The equation of $g(x)$ is in the form $y=mx + b$ where $m$ is the slope and $b$ is the y - intercept. For $g(x)=3x + 1$, the slope $m_g = 3$ and the y - intercept $b_g=1$.

Step4: Compare slopes and y - intercepts

The slope of $f(x)$ ($m_f = 4$) is greater than the slope of $g(x)$ ($m_g=3$), and the y - intercept of $f(x)$ (1) is equal to the y - intercept of $g(x)$ (1).

Answer:

The slope of f(x) is greater than the slope of g(x). The y - intercept of f(x) is equal to the y - intercept of g(x).