The functions ƒ and g are defined as f(x) = 1/5x − 9 and g(x) = 4/5x + 27. If the function h is defined as h(x) = f(x) + g(x), what is the x-intercept of the graph of y = h(x) in the xy-plane?

The functions ƒ and g are defined as f(x) = 1/5x − 9 and g(x) = 4/5x + 27. If the function... | SAT Linear functions Practice

Answer: B. $(-18,0)$

Explanation:1. Define the functions $f(x)$ and $g(x)$ : $f(x) = \dfrac{1}{5}x - 9$ $g(x) = \dfrac{4}{5}x + 27$

Define the function $h(x)$ : $h(x) = f(x) + g(x)$ Substitute the expressions for $f(x)$ and $g(x)$ : $h(x) = (\dfrac{1}{5}x - 9) + (\dfrac{4}{5}x + 27)$
Simplify $h(x)$ : Combine like terms: $h(x) = (\dfrac{1}{5}x + \dfrac{4}{5}x) + (-9 + 27)$ $h(x) = (\dfrac{1+4}{5})x + (18)$ $h(x) = \dfrac{5}{5}x + 18$ $h(x) = x + 18$
Find the x-intercept of the graph of $y=h(x)$ : The x-intercept is the point where the graph crosses the x-axis. At this point, the y-coordinate is $0$ . So, we set $h(x) = 0$ and solve for $x$ . $x + 18 = 0$ $x = -18$
Write the x-intercept as an ordered pair: The x-intercept is $(-18, 0)$ .
Compare with the given options: [A] $(\dfrac{-135}{4},0)$ [B] $(-18,0)$ [C] $(\dfrac{45}{4},0)$ [D] $(18,0)$ Our result matches option B.
Conclusion: The x-intercept of the graph of $y=h(x)$ is $(-18,0)$ .