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The function
f(x)=(2x-1)(3x+7) is graphed in the
xy-plane. Which of the following are the coordinates of an
x-intercept of the graph?
Choose 1 answer:
(A)
(-(3)/(7),0)
(B)
((1)/(2),0)
(C)
(2,0)
(D)
((7)/(3),0)

The function $\newline$ $f(x)=(2x-1)(3x+7)$ is graphed in the $xy$ -plane. Which of the following are the coordinates of an $x$ -intercept of the graph? $\newline$ Choose $1$ answer: $\newline$ (A) $\left(-\frac{3}{7},0\right)$ $\newline$ (B) $\left(\frac{1}{2},0\right)$ $\newline$ (C) $(2,0)$ $\newline$ (D) $\left(\frac{7}{3},0\right)$

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Multiplication with rational exponents

Full solution

Q. The function

\newline

f(x)=(2x-1)(3x+7)

is graphed in the

xy

-plane. Which of the following are the coordinates of an

x

-intercept of the graph?

\newline

Choose

1

answer:

\newline

(A)

\left(-\frac{3}{7},0\right)

\newline

(B)

\left(\frac{1}{2},0\right)

\newline

(C)

(2,0)

\newline

(D)

\left(\frac{7}{3},0\right)

Understand $x$ -intercept: Understand what an $x$ -intercept is. $\newline$ An $x$ -intercept is a point on the graph where the value of $y$ is zero. To find the $x$ -intercept, we set the function $f(x)$ equal to zero and solve for $x$ .
Set function equal: Set the function equal to zero. $\newline$ $f(x) = (2x-1)(3x+7) = 0$ $\newline$ To find the $x$ -intercepts, we need to find the values of $x$ that make this equation true.
Apply zero product property: Apply the zero product property. $\newline$ If the product of two factors is zero, then at least one of the factors must be zero. So we set each factor equal to zero and solve for $x$ . $\newline$ $2x - 1 = 0$ or $3x + 7 = 0$
Solve first equation: Solve the first equation for $x$ . $2x - 1 = 0$ $2x = 1$ $x = \frac{1}{2}$
Solve second equation: Solve the second equation for $x$ . $3x + 7 = 0$ $3x = -7$ $x = -\frac{7}{3}$
Write $x$ -intercepts coordinates: Write the coordinates of the $x$ -intercepts. $\newline$ The $x$ -intercepts occur at the points $(\frac{1}{2}, 0)$ and $(-\frac{7}{3}, 0)$ .

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