Linear Function practice questions

Question 1

Solve $2(x - 1) = 4x + 6$.

Accepted Answer

$2x - 2 = 4x + 6 \Rightarrow -2x = 8 \Rightarrow x = -4$.

Answer

$-4$

Answer

$-2$

Answer

$2$

Answer

$4$

Question 2

The solution of $3x + 5 = 14$ is:

Accepted Answer

$3x = 14 - 5 = 9 \Rightarrow x = 3$.

Answer

$2$

Answer

$3$

Answer

$4$

Answer

$\dfrac{14}{3}$

Question 3

For $f: \mathbb{R} 	o \mathbb{R}$, $f(x) = 2x - 4$, the value of $x$ for which $f(x) = 0$ is:

Accepted Answer

$2x - 4 = 0 \Rightarrow x = 2$.

Answer

$-4$

Answer

$-2$

Answer

$2$

Answer

$4$

Question 4

The solution set of $|2x - 1| = 5$ is:

Accepted Answer

$2x - 1 = 5 \Rightarrow x = 3$, or $2x - 1 = -5 \Rightarrow x = -2$. Solution set: $\{-2, 3\}$.

Answer

$\{3\}$

Answer

$\{-2\}$

Answer

$\{-2, 3\}$

Answer

$\{2, -3\}$

Question 5

The solution set of $2x - 3 > 5$ in $\mathbb{R}$ is:

Accepted Answer

$2x > 8 \Rightarrow x > 4$, so the set is $(4, +\infty)$.

Answer

$(-\infty, 4)$

Answer

$(-\infty, 4]$

Answer

$(4, +\infty)$

Answer

$[4, +\infty)$

Question 6

For which value of $a \in \mathbb{R}$ does the graph of $f(x) = ax + 3$ pass through the point $(2, 7)$?

Accepted Answer

$f(2) = 2a + 3 = 7 \Rightarrow 2a = 4 \Rightarrow a = 2$.

Answer

$1$

Answer

$2$

Answer

$3$

Answer

$7$

Question 7

The slope of the line through $A(1, 2)$ and $B(4, 11)$ is:

Accepted Answer

$m = \dfrac{11 - 2}{4 - 1} = \dfrac{9}{3} = 3$.

Answer

$\dfrac{1}{3}$

Answer

$2$

Answer

$3$

Answer

$9$

Question 8

The pair $(x, y)$ satisfying $\begin{cases} x + y = 5 \ 2x - y = 1 \end{cases}$ is:

Accepted Answer

Adding: $3x = 6 \Rightarrow x = 2$. Then $y = 5 - 2 = 3$. So $(x, y) = (2, 3)$.

Answer

$(1, 4)$

Answer

$(2, 3)$

Answer

$(3, 2)$

Answer

$(4, 1)$

Question 9

The solution to $3x - 7 = 2x + 5$ is:

Accepted Answer

$3x - 7 = 2x + 5$

$3x - 2x = 5 + 7$

$x = 12$.

Answer

$x = -2$

Answer

$x = 2$

Answer

$x = 12$

Answer

$x = -12$

Question 10

Solve $-2x + 5 \le 11$.

Accepted Answer

$-2x + 5 \le 11$

$-2x \le 6$

Divide both sides by $-2$ (flip the sign): $x \ge -3$.

Answer

$x \ge -3$

Answer

$x \le -3$

Answer

$x \ge 3$

Answer

$x \le 3$

Linear Function

Problems & worked solutions

Problem 1 — Linear Function

Problem 2 — Linear Function

Problem 3 — Linear Function

Problem 4 — Linear Function

Problem 5 — Linear Function

Problem 6 — Linear Function

Problem 7 — Linear Function

Problem 8 — Linear Function

Problem 9 — Linear Equations

Problem 10 — Linear Inequalities

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